Equation based state estimator for cooling system controller

ABSTRACT

A system includes a fuel cell stack that receives a fluid, an actuator to increase or decrease a fluid temperature of the fluid, a pipe to facilitate flow of the fluid, and a memory designed to store a model of the fuel cell circuit. The system also includes an ECU that calculates mass flow values of the fluid through the fuel cell stack or the pipe based on a previously-determined mass flow value and the model of the fuel cell circuit. The ECU also calculates a plurality of pressure values corresponding to the fuel cell stack or the pipe based on the plurality of mass flow values and the model, controls the actuator position of the actuator to increase or decrease the fluid temperature based on at least one of the plurality of mass flow values and at least one of the plurality of pressure values.

BACKGROUND 1. Field

The present disclosure relates to systems and methods for controlling atemperature of a fluid that flows through a fuel cell stack of a fuelcell circuit based on feedforward and feedback control of multipleactuators of the fuel cell circuit.

2. Description of the Related Art

As the push for conservation of natural resources and reduced pollutionadvances, various concepts have been discovered to achieve such goals.These concepts range from harvesting wind and sun-based energy tovarious improvements in vehicle design. The vehicle improvements includenew engines designed to improve fuel economy, hybrid vehicles thatoperate using a combination of an engine and a motor-generator tofurther improve fuel economy, fully electric vehicles that operate basedon power stored in a battery, and fuel cell vehicles that generateelectricity by facilitating a chemical reaction.

Many fuel cell vehicles include a fuel cell stack that includes multiplefuel cells. The fuel cells may receive a fuel, which typically includeshydrogen, along with oxygen or another oxidizing agent. The fuel cellstack may facilitate a chemical reaction between the hydrogen andoxygen. This chemical reaction generates electricity and water as abyproduct. The electricity generated by the fuel cell stack may bestored in a battery or directly provided to a motor-generator togenerate mechanical power to propel the vehicle. While fuel cellvehicles are an exciting advance in the automobile industry, thetechnology is relatively new, providing space for improvements to thetechnology.

It is desirable for fuel cells to operate within a predeterminedtemperature range. If the temperature is too low then the power outputby the fuel cells may likewise be relatively low. If the temperature istoo high then the fuel cells may dry out, damaging or destroying thefuel cells.

Thus, there is a need in the art for systems and methods for accuratelycontrolling a temperature of a fuel cell stack use in a vehicle.

SUMMARY

Described herein is a system for heating or cooling a fuel cell circuitof a vehicle. The system includes a fuel cell stack having a pluralityof fuel cells and designed to receive a fluid and to heat the fluid. Thesystem further includes an actuator having an actuator position anddesigned to increase or decrease a fluid temperature of the fluid. Thesystem further includes a pipe designed to facilitate flow of the fluidthrough the fuel cell circuit. The system also includes a memorydesigned to store a model of the fuel cell circuit. The system alsoincludes an electronic control unit (ECU) coupled to the actuator andthe memory. The ECU is designed to calculate a plurality of mass flowvalues of the fluid each corresponding to a mass flow of the fluidthrough the fuel cell stack or the pipe based on a previously-determinedmass flow value and the model of the fuel cell circuit. The ECU is alsodesigned to calculate a plurality of pressure values each correspondingto a pressure of the fluid at an inlet or an outlet of the fuel cellstack or the pipe based on the plurality of mass flow values and themodel of the fuel cell circuit. The ECU is also designed to control theactuator position of the actuator to increase or decrease the fluidtemperature based on at least one of the plurality of mass flow valuesand at least one of the plurality of pressure values.

Also described is a system for heating or cooling a fuel cell circuit ofa vehicle. The system includes a fuel cell stack having a plurality offuel cells and designed to receive a fluid and to heat the fluid. Thesystem also includes a pump designed to pump the fluid through the fuelcell circuit at a pump speed. The system also includes a pipe designedto facilitate flow of the fluid through the fuel cell circuit. Thesystem also includes a memory designed to store a model of the fuel cellcircuit. The system also includes an electronic control unit (ECU)coupled to the pump and the memory. The ECU is designed to calculate aplurality of mass flow values of the fluid each corresponding to a massflow of the fluid through the fuel cell stack, the pump, or the pipebased on a previously-determined mass flow value and the model of thefuel cell circuit. The ECU is also designed to calculate a plurality ofpressure values each corresponding to a pressure of the fluid at aninlet or an outlet of the fuel cell stack, the pump, or the pipe basedon the plurality of mass flow values and the model of the fuel cellcircuit. The ECU is also designed to control the pump to increase ordecrease the pump speed based on at least one of the plurality of massflow values and at least one of the plurality of pressure values.

Also described is a method for heating or cooling a fuel cell circuit ofa vehicle. The method includes storing, in a memory, a model of the fuelcell circuit. The method further includes determining, by the ECU, atemperature control signal corresponding to a desired temperature of afluid within the fuel cell circuit at a fuel cell inlet or a fuel celloutlet of a fuel cell stack of the fuel cell circuit. The method furtherincludes calculating, by an electronic control unit (ECU), a pluralityof temperature values each corresponding to a fluid temperature of fluidat an outlet of a component of the fuel cell circuit based on apreviously-determined temperature value at the outlet, apreviously-determined heat transfer value corresponding to heat transferof the component, and the model of the fuel cell circuit. The methodfurther includes controlling, by the ECU, an actuator position of anactuator to increase or decrease the desired temperature based on theplurality of temperature values and the temperature control signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Other systems, methods, features, and advantages of the presentinvention will be or will become apparent to one of ordinary skill inthe art upon examination of the following figures and detaileddescription. It is intended that all such additional systems, methods,features, and advantages be included within this description, be withinthe scope of the present invention, and be protected by the accompanyingclaims. Component parts shown in the drawings are not necessarily toscale, and may be exaggerated to better illustrate the importantfeatures of the present invention. In the drawings, like referencenumerals designate like parts throughout the different views, wherein:

FIG. 1 is a block diagram illustrating various components of a vehiclehaving a fuel cell circuit capable of generating electricity based on achemical reaction according to an embodiment of the present invention;

FIG. 2 is a block diagram illustrating various features of the fuel cellcircuit of FIG. 1 according to an embodiment of the present invention;

FIG. 3 is a block diagram illustrating various logic components of anelectronic control unit (ECU) of the vehicle of FIG. 1 for increasing ordecreasing a temperature of fluid in the fuel cell circuit according toan embodiment of the present invention;

FIG. 4 is a flowchart illustrating a method for determining a desiredtemperature rate of change of a fuel cell circuit in order to cause atemperature of fluid to reach a desired temperature of the fluidaccording to an embodiment of the present invention;

FIG. 5 is a graph illustrating an exemplary implementation of the methodof FIG. 4 according to an embodiment of the present invention;

FIG. 6 illustrates a lookup table that maps target fuel cell outlettemperatures to temperature differentials according to an embodiment ofthe present invention;

FIG. 7 is a graph illustrating requested and actual temperatures offluid of a fuel cell circuit controlled using a method similar to themethod of FIG. 4 according to an embodiment of the present invention;

FIGS. 8A and 8B are flowcharts illustrating a method feedforward controlof one or more actuator of a fuel cell circuit to heat or cool the fuelcell circuit using according to an embodiment of the present invention;

FIGS. 9A and 9B are flowcharts illustrating a method for estimatingparameters usable to control one or more actuator of a fuel cell circuitaccording to an embodiment of the present invention;

FIG. 10 is a block diagram illustrating a model of a fuel cell circuitused by the method of FIGS. 9A and 9B to estimate the parametersaccording to an embodiment of the present invention;

FIG. 11 is a block diagram illustrating an exemplary flow splittingelement of a fuel cell circuit according to an embodiment of the presentinvention;

FIGS. 12A and 12B are flowcharts illustrating a method for feedbackbased heating or cooling of a fuel cell circuit according to anembodiment of the present invention;

FIG. 13 is a block diagram illustrating a three-way valve controller forfeedback based control of a three-way valve of a fuel cell circuitaccording to an embodiment of the present invention;

FIG. 14 is a block diagram illustrating a pump controller for feedbackbased control of a pump of a fuel cell circuit according to anembodiment of the present invention;

FIGS. 15A and 15B are flowcharts illustrating a method for correcting anestimated parameter that is used to control an actuator of a fuel cellcircuit according to an embodiment of the present invention; and

FIG. 16 is a block diagram illustrating an estimated parametercontroller for correcting an estimated parameter that is used to controla fan of a fuel cell circuit according to an embodiment of the presentinvention.

DETAILED DESCRIPTION

The present disclosure describes systems and methods for heating andcooling fuel cells of a fuel cell circuit. In particular, the presentdisclosure describes systems and methods for estimating a current orrecent state of the fuel cell circuit based on various features. Thesystems provide multiple advantages such as providing near real-time(i.e., within a single discrete time period) estimates of values foreach component of the fuel cell circuit, which provides relatively highaccuracy of the estimates. Estimating the values for the components alsobeneficially reduces costs of building the fuel cell circuit because theestimates reduce the quantity of sensors required to provide accurateresults. The systems also advantageously allow for real-time adjustmentsto the estimates such that errors can be corrected relatively quicklyrather than propagate through the model.

An exemplary system includes multiple components including a fuel cellstack, pipes, a pump, an intercooler, a radiator, and a three-way valve.The system further includes an actuator (which may include the pump andthe three-way valve) that can increase or decrease a fluid temperatureof a fluid within the system. The system includes a memory that stores amodel of the fuel cell circuit including each of the components and thepipes. The system also includes an electronic control unit (ECU). TheECU can estimate various parameters of the system including mass flowrates, temperature values, pressure values, and so forth. The estimatesare based on readings from two temperature sensors as well as currentcommanded actuator positions. The ECU can then control the actuatorsbased on the estimated parameters.

Turning to FIG. 1, a vehicle 100 includes components of a system 101 forcontrolling a temperature of fuel cells of the vehicle. In particular,the vehicle 100 and system 101 include an ECU 102, a memory 104, a speedsensor 106, and a temperature sensor 108. The vehicle 100 furtherincludes a power source 110 which may include at least one of an engine112, a motor-generator 114, a battery 116, or a fuel cell circuit 118.

The ECU 102 may be coupled to each of the components of the vehicle 100and may include one or more processors or controllers, which may bespecifically designed for automotive systems. The functions of the ECU102 may be implemented in a single ECU or in multiple ECUs. The ECU 102may receive data from components of the vehicle 100, may makedeterminations based on the received data, and may control the operationof components based on the determinations.

In some embodiments, the vehicle 100 may be fully autonomous orsemi-autonomous. In that regard, the ECU 102 may control various aspectsof the vehicle 100 (such as steering, braking, accelerating, or thelike) to maneuver the vehicle 100 from a starting location to adestination.

The memory 104 may include any non-transitory memory known in the art.In that regard, the memory 104 may store machine-readable instructionsusable by the ECU 102 and may store other data as requested by the ECU102.

The speed sensor 106 may be any speed sensor capable of detecting datausable to determine a speed of the vehicle 100. For example, the speedsensor 128 may include a GPS sensor or an IMU sensor. The speed sensor128 may also or instead include an angular velocity sensor configured todetect an angular velocity of the wheels of the vehicle 100 or theengine, a speedometer, or the like.

The temperature sensor 108 may include one or more temperature sensorcapable of detecting data usable to determine an ambient temperaturewithin a portion of the vehicle 100 or outside of the vehicle 100. Forexample, the temperature sensor 108 may include a thermocouple, athermometer, an infrared temperature sensor, a thermistor, or the like.

The engine 112 may convert a fuel into mechanical power. In that regard,the engine 112 may be a gasoline engine, a diesel engine, or the like.

The battery 116 may store electrical energy. In some embodiments, thebattery 116 may include any one or more energy storage device includinga battery, a fly-wheel, a super-capacitor, a thermal storage device, orthe like.

The fuel cell circuit 118 may include a plurality of fuel cells thatfacilitate a chemical reaction to generate electrical energy. In thatregard, the electrical energy generated by the fuel cell circuit 118 maybe stored in the battery 116. In some embodiments, the vehicle 100 mayinclude multiple fuel cell circuits including the fuel cell circuit 118.

The motor-generator 114 may convert the electrical energy stored in thebattery (or electrical energy received directly from the fuel cellcircuit 118) into mechanical power usable to propel the vehicle 100. Themotor-generator 114 may further convert mechanical power received fromthe engine 112 or wheels of the vehicle 100 into electricity, which maybe stored in the battery 116 as energy and/or used by other componentsof the vehicle 100. In some embodiments, the motor-generator 114 mayalso or instead include a turbine or other device capable of generatingthrust.

The body of the vehicle 100 may include a grill 120 located at a frontof the vehicle. The grill 120 may receive an airflow 122. The speed ofthe airflow 122 may directly correspond to the speed of the vehicle 100.For example, if a headwind of 5 miles per hour (mph) exists outside ofthe vehicle 100 and the vehicle is traveling at 50 mph then the speed ofthe airflow 122 will be approximately 55 mph.

Turning now to FIG. 2, additional details of the fuel cell circuit 118are illustrated. The fuel cell circuit 118 includes a fuel cell stack200 having a plurality of fuel cells. The fuel cells may each facilitatea chemical reaction to generate electricity. The reaction may generateheat. Furthermore, a fluid may flow through the fuel cell stack 200 andmay transfer at least some of the heat away from the fuel cell stack200. In that regard, the fuel cell stack 200 may include an inlet 228for receiving the fluid and an outlet 230 through which the fluid exitsthe fuel cell stack 200.

It may be desirable for the fuel cell stack 200 to operate within apredetermined temperature range. For example, it may be desirable forthe fuel cells of the fuel cell stack 200 to operate between 50 degreesCelsius (50 degrees C., 122 degrees Fahrenheit (122 degrees F.)) and 80degrees C. (176 degrees F.).

The fuel cell stack 200 may generate more electrical energy atrelatively high temperatures (i.e., when the temperature is closer to 80degrees C. than 50 degrees C.). However, the fuel cell stack 200 mayundesirably lose moisture (i.e., may dry out) when operated at theserelatively high temperatures. In that regard, it may be desirable forthe fuel cell stack 200 to operate closer to 80 degrees C. when arelatively large amount of electrical energy is requested, and closer to50 degrees C. when a relatively small amount of electrical energy isrequested. The fuel cell circuit 118 includes various features forincreasing or decreasing the temperature of the fuel cell stack 200.

The fuel cell circuit 118 may further include an intercooler 202. Theintercooler 202 may be oriented in parallel with the fuel cell stack200. The intercooler 202 may receive a hot airflow 203 (i.e., an airflowhaving a greater temperature than the temperature of the fluid withinthe intercooler 202) and may transfer heat from the hot airflow 203 tothe fluid. Accordingly, the fuel cell stack 200 and the intercooler 202may be considered heating elements of the fuel cell circuit 118 as theyboth increase the temperature of the fluid. All of the fluid within thefuel cell circuit 118 eventually flows through the combination of thefuel cell stack 200 and the intercooler 202 as shown by an arrow 205.

The fuel cell circuit 118 may further include a three-way valve 204. Thefuel cell circuit 118 may also include one or more radiator 210 alongwith a bypass branch 206 that bypasses the one or more radiator 210. Thethree-way valve 204 may divide the fluid between the radiators 210 andthe bypass branch 206 based on a valve position of the three-way valve204. The three-way valve 204 may have multiple valve positions eachdividing the flow between the bypass branch 206 and the radiators 210 atdifferent ratios.

For example, the three-way valve 204 may have a first position in which80 percent (80%) of the fluid flows through the bypass branch 206 (asshown by an arrow 207) and 20% of the fluid flows through the radiators210 (as shown by an arrow 209). The three-way valve 204 may further havea second position in which 70% of the fluid flows through the bypassbranch 206 and 30% of the fluid flows through the radiators 210. Thethree-way valve 204 may have multiple discrete valve positions or mayhave infinite continuous valve positions (i.e., may direct any valuebetween 0% and 100% of the fluid through each of the bypass branch 206or the radiators 210).

The fluid that flows through the bypass branch 206 may avoid theradiators 210, thus allowing a majority of heat within the fluid toremain in the fluid. An ionizer 208 may receive some of the fluid thatflows through the bypass branch 206. The ionizer 208 may function as anion exchanger and may remove ions from the fluid to reduce conductivity.In that regard, the ionizer may be referred to as a de-ionizer.

The radiators 210 may transfer heat away from the fluid to a gas (suchas air) flowing over or past the radiators 210. In that regard, theradiators 210 may be referred to as cooling elements of the fuel cellcircuit 118.

In some embodiments, the radiators 210 may include a main radiator 212and two secondary radiators 214, 216. A fan 218 may be oriented in sucha manner as to direct a flow of gas 219 over the radiators 210. In someembodiments, the fan 218 may only direct the flow of gas 219 over themain radiator 212. The main radiator 212 has a fluid inlet 232 in whichthe fluid flows into the main radiator 212 and a fluid outlet 234 inwhich the fluid flows out of the main radiator 212. The main radiator212 may further include an air inlet 236 that receives the gas 219(i.e., airflow) from the fan 218 as well as an air outlet 238 in whichthe airflow exits the main radiator 212.

Referring briefly to FIGS. 1 and 2, one or more of the radiators 210 mayfurther receive the airflow 122 received via the grill 120 of thevehicle 100. As mentioned above, the velocity of the airflow 122corresponds to a speed of the vehicle 100. As the speed of the vehicle100 increases, the velocity of the airflow 122 further increases, thusincreasing the transfer of heat away from the fluid.

Returning reference to FIG. 2, the fuel cell circuit 118 may furtherinclude a pump 220. The pump 220 may include any pump capable of forcingthe fluid through the fuel cell circuit 118. For example, the pump 220may include a hydraulic pump, a diaphragm pump, a piston pump, a rotarygear pump, or the like.

The fuel cell circuit 118 may further include a reservoir 240. Thereservoir may include a volume in which the fluid, such as a coolant, isstored. The fluid may be provided to the fuel cell circuit 118 from thereservoir 240. In some embodiments, the reservoir 240 may include a portthrough which a user of the vehicle may provide the fluid to thereservoir 240.

The fuel cell circuit 118 may further include two temperature sensorsincluding a first temperature sensor 224 and a second temperature sensor226. The first temperature sensor 224 may detect the temperature of thefluid exiting the fuel cell stack 200 at the outlet 230. The secondtemperature sensor 226 may detect the temperature of the combined fluidexiting the radiators 210. In some embodiments, greater or fewertemperature sensors may be used, and the temperature sensors may bepositioned at additional or alternative locations.

Referring again to FIGS. 1 and 2, the ECU 102 may determine a targettemperature of the fuel cell stack 200 based on a received power requestof the vehicle 100. As described above, it may be desirable for thetemperature of the fuel cell stack 200 to increase when a relativelylarge amount of power is requested from the fuel cell stack 200. This isbecause the increased temperature corresponds to an increased poweroutput of the fuel cell stack 200. Likewise, it may be desirable for thetemperature of the fuel cell stack 200 to decrease when a relativelysmall amount of power is requested from the fuel cell stack 200 in orderto retain moisture in the fuel cell stack 200.

The ECU 102 may also receive the detected temperatures from the firsttemperature sensor 224 and the second temperature sensor 226. The ECU102 may then control the actuators of the fuel cell circuit 118 (thethree-way valve 204, the fan 218, and the pump 220) to cause thetemperature of the fuel cell stack 200 (such as the temperature of thefluid at the outlet 230) to increase or decrease. The ECU 102 may causethe temperature to increase or decrease towards the target temperaturebased on the target temperature and the detected temperatures.

The three-way valve 204 may be used to adjust the temperature of thefluid by directing more of the fluid through the bypass branch 206 orthrough the radiators 210. For example, if the three-way valve 204increases a flow of the fluid through the bypass branch 206 then theoverall temperature of the fluid may increase because it is directedback towards the heating elements without significant loss of heat.Similarly, if the three-way valve 204 increases a flow of the fluidthrough the radiators 210 then the overall temperature of the fluid maydecrease because more fluid is directed through the radiators 210 wherethermal energy may be removed from the fluid.

The fan 218 may likewise be used to adjust the temperature of the fluidby increasing or decreasing the flow of gas 219 over the main radiator212. For example, if the speed of the fan 218 is increased (resulting ina greater quantity of gas 219 flowing over the main radiator 212) thenthe temperature of the fluid may decrease as more thermal energy istransferred out of the fluid. Similarly, if the speed of the fan 218 isdecreased then the temperature of the fluid may increase as less thermalenergy is transferred out of the fluid.

The pump 220 may also be used to indirectly adjust the temperature ofthe fluid by increasing or decreasing a flow rate, such as a mass flowrate, of the fluid through the fuel cell circuit 118. As the flow rateincreases, heat transfer between the fluid and the various componentsincreases, which may result in an increase or decrease in temperaturebased on how much of the fluid flows through the bypass branch 206 orthe radiators 210, and based on a temperature of the fuel cell stack200. Thus, the temperature of the fluid may correspond to the flow rateof the fluid.

Referring now to FIGS. 2 and 3, the ECU 102 may include a temperaturecontrol system 303 that controls the temperature of the fuel cellcircuit 118. The temperature control system 303 may be implemented usingspecifically designated hardware of the ECU 102, or may be implementedusing general hardware of the ECU 102.

The temperature control system 303 may include an upper controller 300,a state mediator 304, a state governor 308, a feedforward control 312, afeedback control 316, a state estimator 320, an observer 322, and anactuator control 330. The temperature control system 303 may receive aninput, such as a power request 301, and may generate an output, such asan actuator control signal 334.

The upper controller 300 may receive the power request 301. The uppercontroller 300 may then identify a target temperature of the fuel cellstack 200 based on the power request 301. For example, if the powerrequest is relatively large then the upper controller 300 may set atarget temperature to be relatively high, such as 75 degrees C. (167degrees F.). Likewise, if the power request is relatively small then theupper controller 300 may set a target temperature to be relatively low,such as 55 degrees C. (131 degrees F.). The upper controller 300 maythen output an unfiltered target fuel cell temperature 302.

The state mediator 304 may receive the unfiltered target fuel celltemperature 302. The state mediator 304 may filter the received signaland output a target fuel cell temperature 306. The state mediator 304may filter the unfiltered target fuel cell temperature 302 for variousreasons. For example, the filtering may remove noise on the signal, mayact as a bandpass filter to ensure that the target fuel cell temperature306 is within a safe temperature range, or the like. The safetemperature range may correspond to a temperature range at which thetemperature is unlikely to damage components of the fuel cell circuit118 (i.e., such as by overheating or drying out) and at which the fuelcell circuit 118 is capable of generating power.

The state governor 308 may receive the target fuel cell temperature 306.The state governor 308 may generally dictate how fast the temperature ofthe fluid in the fuel cell circuit 118 should respond to the temperaturechange request (i.e., how fast the temperature should increase ordecrease). The state governor 308 may output a temperature rate ofchange 310 corresponding to a desired rate of temperature change of thefluid (such as at the inlet 228 or the outlet 230 of the fuel cell stack200). For example, the temperature rate of change 310 may be measured indegrees (e.g., degrees C.) per second.

The state estimator 320 may receive inputs including sensor values 326and current actuator positions 328 (or commanded actuator positions) andmay estimate conditions at various locations of the fuel cell circuit118. The sensor values may include, for example, temperatures detectedfrom the first temperature sensor 224 and the second temperature sensor226. The actuator positions 328 may be received from the actuators 332themselves (the pump 220, the three-way valve 204, and the fan 218) orfrom the actuator control signal 334.

The fuel cell circuit 118 includes relatively few sensors. Additionaldata is desirable in order to provide optimal control of the actuators332. In that regard, the state estimator 320 may calculate or predictthe additional data (i.e., current conditions) based on the sensorvalues 326 and the actuator positions 328. For example, the stateestimator 320 may calculate or predict temperatures at locations of thefuel cell circuit 118 in which temperature sensors are not present. Asanother example, the state estimator 320 may calculate or predictpressure of the fluid at various locations of the fuel cell circuit 118.As yet another example, the state estimator 320 may further calculate orpredict quantities of heat added to or subtracted from the fluid by thevarious elements of the fuel cell circuit 118. The state estimator 320may output calculated or predicted values 324 corresponding to currentconditions of the fuel cell circuit 118.

The feedforward control 312 may receive the temperature rate of change310 from the state governor 308 along with the calculated or predictedvalues 324 from the state estimator 320. In some embodiments, thefeedforward control 312 may further receive the detected temperaturesfrom the temperature sensors. The feedforward control 312 may determinedesired positions of the actuators 332 to achieve the desiredtemperature rate of change 310 of the fluid of the fuel cell circuit118. The feedforward control 312 may determine these desired positionsbased on the received temperature rate of change 310 and the calculatedor predicted values 324. The feedforward control 312 may outputfeedforward control signals 314 corresponding to the determined desiredpositions of the actuators 332.

The feedback control 316 may also receive the temperature rate of change310 from the state governor 308 along with the calculated or predictedvalues 324 from the state estimator 320. In some embodiments, thefeedback control 316 may further receive the detected temperatures fromthe temperature sensors. The feedback control 316 may identify whetherthe actuators 332 are achieving the desired temperature rate of change310. The feedback control 316 may further generate feedback controlsignals 318 that correspond to adjustments to the actuators 332 to closethe gap between a measured temperature rate of change and the desiredtemperature rate of change 310.

The observer 322 may operate as feedback control for the radiators 210.In that regard, the observer may determine a difference between adetected temperature at the outlet 227 of the radiators 210 and anestimated temperature at the outlet 227 as determined by the stateestimator 320. The observer 322 may then change values determined by thestate estimator 320 to cause the estimated temperature to be closer invalue to the detected temperature.

The actuator control 330 may receive the feedforward control signals 314and the feedback control signals 318 and generate actuator controlsignals 334 based on the combination of the feedforward control signals314 and the feedback control signals 318. One or more of the actuatorcontrol signals 334 may be transmitted to each of the actuators 332. Forexample, the actuator control signals 334 may include a first signalthat controls a valve position of the three-way valve 204, a secondsignal that controls a fan speed of the fan 218, and a third signal thatcontrols a pump speed of the pump 220. In some embodiments, the actuatorcontrol 330 may generate the actuator control signals 334 by adding thefeedforward control signals 314 and the feedback control signals 318.

Referring now to FIG. 4, a method 400 for determining a desiredtemperature rate of change of a fuel cell circuit, such as the fuel cellcircuit 118 of FIG. 2, is shown. The method 400 may be performed by astate governor, such as the state governor 308 of FIG. 3.

In block 402, one or more temperature sensor of a fuel cell circuit maydetect a current temperature corresponding to a temperature of fluidwithin the fuel cell circuit. For example, the first temperature sensor224 may detect a temperature of the fluid at the outlet 230 of the fuelcell stack 200, and the second temperature sensor 226 may detect atemperature of the fluid at the outlet 227 of the radiators.

In block 404, the ECU of the vehicle may estimate or calculateadditional values corresponding to the fuel cell circuit. For example,the state estimator 320 of FIG. 3 may estimate or calculate values basedon the detected temperatures and the current actuator positions. Theadditional values may include, for example, temperatures of the fuelcell circuit at locations other than the locations of the temperaturesensors, pressures at various locations along the fuel cell circuit, orthe like.

In block 406, if the vehicle or fuel cell stack is warming up from acold start (i.e., such as when the vehicle is initially turned on) thenthe ECU may determine a fuel cell inlet temperature command value. TheECU may determine the target fuel cell inlet temperature based on thetemperatures detected in block 402 and the values calculated in block404. For example, the target fuel cell inlet temperature may bedetermined using equation 1 below.

$\begin{matrix}{T_{{FC}_{{in}_{cmd}}} = {\min \left( {{\max \left( {{T_{{FC}_{cmd}} - {\Delta \; T_{{FC}_{tgt}}}},T_{{FC}_{{in}\mspace{14mu} {cmd}\mspace{14mu} {previous}}}} \right)},T_{{FC}_{{in}\mspace{14mu} {tgt}}}} \right)}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In equation 1,

T_(FC_(in_(cmd)))

corresponds to the target fuel cell inlet temperature. T_(FC) _(cmd)corresponds to the target fuel cell outlet temperature, which is set tobe equal to the detected fuel cell outlet temperature of the fuel cellstack during the warm-up. ΔT_(FC) _(tgt) corresponds to a targettemperature difference between the fuel cell inlet temperature and thefuel cell outlet temperature, and is determined by the upper controller.T_(FC) _(in cmd previous) corresponds to the target fuel cell inlettemperature determined during a previous calculation of equation 1.T_(FC) _(in tgt) corresponds to a final target fuel cell inlettemperature, which is the final desired operating temperature of thefluid at the inlet.

After the fuel cell circuit has warmed up, the final target fuel cellinlet temperature remains relatively constant, and thus is a stable(i.e., unchanging) value during operation of the fuel cell circuit.Stated differently, the final target fuel cell inlet temperature remainsrelatively unchanged throughout operation of the vehicle after theinitial warmup.

Referring briefly to FIG. 5, a graph 500 illustrates implementation ofequation 1 by the ECU to set the target fuel cell inlet temperature. Inparticular, the graph 500 illustrates the current fuel cell outlettemperature 502, the target fuel cell outlet temperature 504, thecurrent fuel cell inlet temperature 506, and the target fuel cell inlettemperature 508. The graph 500 further illustrates the targettemperature difference 510 between the fuel cell inlet temperature andthe fuel cell outlet temperature, and the current temperature difference512.

During a first segment 514 of an initial warm-up, the target fuel cellinlet temperature 508 increases simultaneously with the current fuelcell outlet temperature 502. The target fuel cell inlet temperature 508is calculated as the difference between the current fuel cell outlettemperature 502 and the target temperature difference 510.

At the beginning of a second segment 516, the upper controller hasincreased the target temperature difference 510. Because the target fuelcell inlet temperature 508 is calculated as the difference between thecurrent fuel cell outlet temperature 502 and the target temperaturedifference 510, the target fuel cell inlet temperature 508 remainsconstant for a period of time 518 until the current temperaturedifference 512 is equal to the target temperature difference 510. Thetarget fuel cell inlet temperature 508 begins increasing again when thecurrent temperature difference 512 is equal to or exceeds the targettemperature difference 510.

The target temperature difference 510 decreases at the beginning of athird segment 520 of the warm-up. Accordingly, the target fuel cellinlet temperature 508 increases to again be equal to the differencebetween the current fuel cell outlet temperature 502 and the reducedtarget temperature difference 510.

By setting the target fuel cell inlet temperature 508 to be equal to theminimum of the calculated value or the final target fuel cell inlettemperature, equation 1 ensures that the target fuel cell inlettemperature 508 fails to exceed the final target fuel cell inlettemperature.

Referring now to FIGS. 4 and 5 and in block 408, the ECU may control oneor more actuator of the fuel cell circuit to increase a temperature ofthe fluid to cause the current fuel cell inlet temperature to be equalto the target fuel cell inlet temperature. For example, the ECU maycontrol one or more of a three-way valve, a radiator fan, or a pump toincrease the temperature of the fluid. As shown in the graph 500, thecurrent fuel cell inlet temperature 506 remains relatively similar tothe target fuel cell inlet temperature 508 during the entire warm-up.

Returning reference to FIG. 4, the ECU may receive or calculate a targetfuel cell outlet temperature in block 410. The target fuel cell outlettemperature may correspond to a desired temperature of the fluid at theoutlet of the fuel cell stack and may be determined by one or more of anupper controller or a state mediator of the ECU. As shown, the ECU maycontrol the temperature of the fluid of the fuel cell circuit using atarget fuel cell inlet temperature during the initial warm-up, and maycontrol the temperature of the fluid of the fuel cell circuit using atarget fuel cell outlet temperature during normal operation after theinitial warm-up.

In block 412, the ECU may calculate a temperature differential. Thetemperature differential may correspond to a difference between thetarget fuel cell outlet temperature and the current fuel cell outlettemperature.

In block 414, the ECU may determine a temperature rate of change. Thetemperature rate of change may correspond to a desired rate of increaseor decrease of the temperature of the fluid at a particular location,such as at the outlet of the fuel cell stack. The temperature rate ofchange may be represented as dT/dt (“T” representing temperature and “t”representing time), and may have units of degrees per second (such asdegrees C./second).

The ECU may determine the temperature rate of change based on the targetfuel cell outlet temperature received from the upper controller, thetemperature differential calculated in block 412, and a desire toconserve energy. For example, if the temperature differential isrelatively low it may be desirable to use relatively little energy towarm-up the fuel cell stack in order to increase energy efficiency ofthe vehicle.

In some embodiments, the ECU may determine the temperature rate ofchange by comparing the target fuel cell outlet temperature and thetemperature differential to a lookup table stored in a memory.

Referring now to FIG. 6, an exemplary lookup table 600 is shown. The Yaxis of the lookup table 600 corresponds to the target fuel cell outlettemperature and the X axis corresponds to the temperature differential.A negative temperature differential indicates that it is desirable forthe current fuel cell outlet temperature to decrease and a positivetemperature differential indicates that it is desirable for the currentfuel cell outlet temperature to increase. Likewise, a negativetemperature rate of change corresponds to a decreasing temperature rate,and a positive temperature rate of change corresponds to an increasingtemperature rate.

As shown, the lookup table 600 includes a plurality of regions. Theregions include a rapid temperature decrease region 602, a reducedenergy temperature decrease region 604, an error correction region 606,a reduced energy temperature increase region 610, and a rapidtemperature increase region 610. The rapid temperature decrease region602 and the rapid temperature increase region 612 each correspond to arelatively high temperature rate of change.

The relatively high temperature rates of change may be selected based oncapabilities of the system. For example, the rapid temperature decreaseregion 602 may have a temperature rate of change of 1 degree C. persecond, which may be a maximum temperature decrease rate that the fuelcell circuit is capable of achieving. Likewise, the rapid temperatureincrease region 612 may have a maximum temperature rate of change of 4.3degrees C. per second, which may be a maximum temperature increase ratethat the fuel cell circuit is capable of achieving.

The temperature rates of change in the rapid temperature decrease region602 may be desirable when the fuel cell outlet temperature is to bedecreased significantly. In that regard, the relatively high rate oftemperature decrease in the rapid temperature decrease region 602 mayreduce the likelihood of the fuel cell stack drying out. Likewise, thetemperature rate of change in the rapid temperature increase region 610may be desirable when the fuel cell outlet temperature is to beincreased significantly. In that regard, the relatively high rate oftemperature increase in the rapid temperature increase region 610 mayallow the fuel cell stack to provide a relatively large amount of powerwhen a relatively large power request is received.

The relatively high temperature rates of change may be relatively energyinefficient and thus may be undesirable for relatively small temperaturechanges. In that regard, the reduced energy rates of change maycorrespond to temperature increase and decrease rates that arerelatively energy efficient. Accordingly, the reduced energy rates ofchange may be less than the relatively high temperature rates of change,but may also be more energy-efficient than the relatively hightemperature rates of change.

The error correction rates of change may be less than the reduced energyrates of change, and may be more energy efficient than the reducedenergy rates of change. In that regard, the error correction rates ofchange may be utilized to correct relatively small differences betweenthe target fuel cell outlet temperature and the actual fuel cell outlettemperature.

Returning reference to FIG. 4, the ECU may control the one or moreactuator of the fuel cell circuit to increase or decrease thetemperature of the fluid based on the temperature rate of change thatwas determined in block 414.

Referring now to FIG. 7, a graph 700 illustrates a power request signal702 corresponding to a power request of the vehicle. The graph 700further illustrates a current fuel cell outlet temperature 704 and atarget fuel cell outlet temperature 706, along with a current fuel cellinlet temperature 708 and a target fuel cell inlet temperature 710. Asdescribed above and shown in FIG. 7, the target fuel cell inlettemperature 710 remains constant throughout operation of the vehicle. Inthat regard, the current fuel cell inlet temperature 708 also remainsrelatively constant.

The ECU may control the current fuel cell outlet temperature based onthe previously determined temperature rate of change. During a firsttime window 712 the power request signal 702 is low, corresponding to alack of power request. Accordingly, the target fuel cell outlettemperature 706 remains at a relatively low value throughout the firsttime window 712, and the current fuel cell outlet temperature 704remains relatively the same as the target fuel cell outlet temperature706.

At the beginning of a second time window 714, the power request signal702 increases to a relatively low value, corresponding to a relativelylow amount of energy being requested from the fuel cell stack.Accordingly, the target fuel cell outlet temperature 706 increases by arelatively small amount. Accordingly, the temperature differential maybe relatively small such that the temperature rate of change fallswithin the reduced energy temperature increase region as a rapidtemperature increase is unnecessary. Because the ECU controls theactuators to increase the temperature at the reduced energy temperaturerate of change, the current fuel cell outlet temperature 704 mayincrease gradually during the second time window 714.

At the beginning of a third time window 716, the power request signal702 increases to a wide open throttle (WOT) power request whichcorresponds to a relatively large amount of energy being requested fromthe fuel cell stack. Accordingly, the target fuel cell outlettemperature 706 increases by a relatively large amount. As a result, thetemperature differential may be relatively large such that thetemperature rate of change falls within the rapid temperature increaseregion to facilitate the relatively large amount of energy requested ofthe fuel cell stack.

Because the ECU controls the actuators to increase the temperature atthe rapid temperature rate of change, the current fuel cell outlettemperature 704 may increase relatively rapidly at the beginning of thethird time window 716. Accordingly, the current fuel cell outlettemperature 704 may reach the target fuel cell outlet temperature 706relatively quickly.

At the beginning of a fourth time window 718, the power request signal702 decreases to a low power request which corresponds to a relativelysmall amount of energy being requested from the fuel cell stack.Accordingly, the target fuel cell outlet temperature 706 decreases by arelatively large amount. The temperature differential corresponding tothis rapid decrease of the target fuel cell outlet temperature 706 maybe relatively large such that the temperature rate of change fallswithin the rapid temperature decrease region to prevent dry out of thefuel cell stack. Because the ECU controls the actuators to decrease thetemperature at the rapid temperature rate of change, the current fuelcell outlet temperature 704 may decrease relatively rapidly at thebeginning of the fourth time window 718.

After a relatively short period of time 720 the ECU may determine thatthe current fuel cell outlet temperature 704 is sufficiently small thatdry out of the fuel cell stack is unlikely to occur. Furthermore, thetemperature differential has decreased after the period of time 720 dueto the decreased current fuel cell outlet temperature 704. Thus, thetemperature rate of change may change to the reduced energy temperaturedecrease region in order to conserve energy. Thus, after the period oftime 720 has elapsed, the current fuel cell outlet temperature 704 maydecrease more gradually due to the newly reduced temperature rate ofchange.

Referring now to FIGS. 8A and 8B, a method 800 for feedforward controlof one or more actuator of the fuel cell circuit to heat or cool thefuel cell circuit is shown. The method 800 may be performed, forexample, by a feedforward control of an ECU such as the feedforwardcontrol 312 of the ECU 102 of FIG. 3.

In block 802, the ECU may determine a temperature rate of change. Thetemperature rate of change may be determined using a method similar tothe method 400 of FIG. 4. In some embodiments, the ECU may also orinstead determine or receive another temperature control signalcorresponding to a desired pressure(s) at various locations along thefuel cell circuit, or the like.

In block 806, the ECU may calculate a desired mass flow rate of thefluid that corresponds to the temperature rate of change. The ECU maycalculate the desired mass flow rate based on the temperature rate ofchange determined in block 802 as well as the estimated or calculatedvalues determined in block 804. For example, the ECU may calculate thedesired mass flow rate using an equation similar to equation 2 below:

$\begin{matrix}{{\overset{.}{m}}_{FF} = \frac{{V_{eq}\rho_{eq}c_{eq}\frac{dT}{dt}} - Q_{FC}}{\left( {{c\left( {\Delta T} \right)} + {\frac{1}{\rho}\left( {P_{{FC}_{in}} - P_{{FC}_{out}}} \right)}} \right)}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

In equation 2, {dot over (m)}_(FF) represents the desired mass flow rateof the fluid through a fuel cell stack, such as the fuel cell stack 200of FIG. 2. V_(eq) represents an equivalent volume of the fluid(including a coolant and water) and the fuel cell stack, and is aphysical property of the fluid and fuel cell stack. ρ_(eq) represents anequivalent density of the fluid and the fuel cell stack and may bereceived from the state estimator in block 804. c_(eq) represents anequivalent specific heat of the fluid in the fuel cell stack and mayalso be received from the state estimator in block 804.

$\frac{dT}{dt}$

represents the temperature rate of change calculated in block 802.Q_(FC) represents an amount of heat generated by the fuel cell stack andmay be received from the state estimator in block 804. c represents thespecific heat of the fluid and may be received from the state estimatorin block 804. ΔT represents a difference between the target fuel cellinlet temperature and the target fuel cell outlet temperature (T_(FC)_(in cmd) −T_(FC) _(cmd) ) and may be received from a state governor,such as the state governor 308 of FIG. 3, or from a state estimator inblock 804. ρ represents the density of the fluid and may be receivedfrom the state estimator in block 804. P_(FC) _(in) represents a currentpressure of the fluid at an inlet of the fuel cell stack and P_(FC)_(out) represents a current pressure of the fluid at an outlet of thefuel cell stack, both of which may be received from the state estimatorin block 804.

Referring to FIG. 2 and as described above, {dot over (m)}_(FF)represents the desired mass flow rate of the fluid through the fuel cellstack 200. However, the fluid output by the pump 220 is received by boththe fuel cell stack 200 and the intercooler 202. In that regard, it isdesirable for the ECU to further calculate the desired mass flow rate ofthe fluid through the pump 220 (i.e., a sum of the mass flow ratethrough the fuel cell stack 200 and the intercooler 202), also referredto as a total desired mass flow rate. The ECU may utilize a stateestimator, such as the state estimator 320 of FIG. 3, to calculate thetotal desired mass flow rate through the pump 220.

Returning reference to FIGS. 8A and 8B, the ECU may determine a desiredpump speed of the pump based on the total desired mass flow ratecalculated in block 808. In some embodiments, the memory of the vehiclemay store a lookup table that maps desired mass flow rates tocorresponding pumps speeds. In these embodiments, the ECU may comparethe desired mass flow rate calculated in block 806 to the lookup tableand retrieve the pump speed that corresponds to the desired mass flowrate.

In some embodiments, the ECU may determine the desired pump speed basedon a sum of the total desired mass flow rate calculated in block 806 andan adjustment to the total desired mass flow rate calculated by afeedback control, such as the feedback control 316 of FIG. 3. In thatregard, the desired pump speed may be a function of the total desiredmass flow rate, the adjustment to the total desired mass flow rate, anda difference in pressure between an outlet of the pump and an inlet ofthe pump. The difference in pressure between the outlet of the pump andthe inlet of the pump may correspond to a total pressure drop over thefuel cell circuit. The ECU may compare the results of the function to alookup table and retrieve the desired pump speed from the lookup tablebased on the comparison.

In block 810, the ECU may control the pump to pump the fluid through thefuel cell circuit at the desired pump speed determined in block 808.

In block 812, the ECU may calculate a desired fluid split ratio of thefluid that is output by a three-way valve, such as the three-way valve204 of FIG. 2. Referring briefly to FIG. 2, the desired fluid splitratio may correspond to a ratio of fluid that is directed towards theradiators 210 to fluid that is directed through the bypass branch 206.In some embodiments, the desired fluid split ratio may represent apercentage of the total fluid output by the three-way valve 204 that isdirected towards the radiators 210, or may represent a percentage of thetotal fluid output by the three-way valve 204 that is directed throughthe bypass branch 206.

Returning reference to FIGS. 8A and 8B, the ECU may calculate thedesired fluid split ratio using an equation similar to equation 3 below.

$\begin{matrix}{\left. \rightarrow Z_{FF} \right. = \frac{\left( {T_{{pump}\mspace{14mu} {in}} - T_{bypass}} \right)}{\left( {T_{{rad}\mspace{14mu} {out}} - T_{bypass}} \right)}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

In equation 3, Z_(FF) represents the desired fluid split ratiocalculated by the feedforward control and corresponds to a percentage ofthe total fluid output by the three-way pump that is directed throughthe radiators. T_(pump in) represents a temperature of an inlet of thepump and may be calculated by the state estimator in block 804.T_(bypass) represents a temperature of the fluid directed through thebypass branch, which may be calculated at an outlet of the three-wayvalve that outputs fluid to the bypass branch, and may be calculated bythe state estimator in block 804. T_(rad out) corresponds to atemperature of the fluid at an outlet of the radiators and may bedetected using a temperature sensor, such as the second temperaturesensor 226 of FIG. 2.

In block 814, the ECU may determine a desired valve position of thethree-way valve based on the desired fluid split ratio calculated inblock 812. In some embodiments, the memory of the vehicle may store alookup table that maps desired fluid split ratios to corresponding valvepositions. In these embodiments, the ECU may compare the desired fluidsplit ratio calculated in block 812 to the lookup table and retrieve thedesired valve position that corresponds to the desired fluid splitratio.

In some embodiments, the ECU may determine the desired valve positionbased on a sum of the desired fluid split ratio calculated in block 812and an adjustment to the desired fluid split ratio calculated by thefeedback control. In that regard, the desired valve position may be afunction of the desired fluid split ratio and the adjustment to thedesired fluid split ratio. The ECU may compare the results of thefunction to a lookup table and retrieve the desired valve position basedon the comparison.

In block 816, the ECU may control the three-way valve to have thedesired valve position that was determined in block 814.

In block 818, the ECU may calculate a desired amount of thermal energy(i.e., heat) to be removed by radiators of the fuel cell circuit(including main and secondary radiators such as the main radiator 216and the secondary radiators 214 and 216 of FIG. 2). The ECU maycalculate the desired amount of thermal energy to be removed by theradiators using an equation similar to equation 4 below.

$\begin{matrix}{Q_{{rad}_{total}} = {{V_{eq}\rho_{eq}c_{eq}\frac{dT}{dt}} - Q_{FC} - Q_{IC}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

In equation 4, Q_(rad) _(total) represents the desired amount of thermalenergy (i.e., heat) to be removed by all radiators of the fuel cellcircuit. V_(eq) represents an equivalent volume of the fluid (includinga coolant and water) and the fuel cell stack, and is a physical propertyof the fluid and fuel cell stack. ρ_(eq) represents an equivalentdensity of the fluid and the fuel cell stack and may be received fromthe state estimator in block 804. c_(eq) represents an equivalentspecific heat of the fluid and the fuel cell stack and may also bereceived from the state estimator in block 804.

$\frac{dT}{dt}$

represents the temperature rate of change calculated in block 802.Q_(FC) represents an amount of heat generated by the fuel cell stack(i.e., a stack heating amount) and may be received from the stateestimator in block 804. Q_(IC) represents an amount of heat generated bythe intercooler (i.e., an intercooler heating amount) and may bereceived from the state estimator in block 804.

In block 820, the ECU may calculate a desired amount of thermal energyto be removed from the main radiator by the fan. The ECU may make thiscalculation using the desired amount of thermal energy to be removed byall radiators that was calculated in block 818. The ECU may calculatethe desired amount of thermal energy to be removed from the mainradiator by the fan using an equation similar to equation 5 below.

Qrad_(main) _(fan) =Q _(rad) _(total) −Q _(rad) _(sub1) −Qrad_(sub2)−Qrad_(main) _(amb)   Equation 5:

In equation 5, Qrad_(main) _(fan) represents the desired amount ofthermal energy to be removed from the main radiator by the fan. Q_(rad)_(total) represents the desired amount of thermal energy to be removedby all radiators that was calculated in block 818. Q_(rad) _(sub1)represents an amount of thermal energy dissipated by the first secondaryradiator and Q_(rad) _(sub2) represents an amount of thermal energydissipated by the second secondary radiator (i.e., a secondary amount ofthermal energy). Q_(rad) _(sub1) and Q_(rad) _(sub2) may be receivedfrom the state estimator in block 804, and may be calculated using anequation that is based on a temperature and velocity of ambient air thatflows over the secondary radiators. Qrad_(main) _(amb) represents anamount of thermal energy dissipated by the main radiator due to theambient air (i.e., airflow other than that generated by the fan).

Because the fan does not blow the air over the secondary radiators, thesecondary radiators may reject heat into an air flow received through agrill of the vehicle, which may vary based on a speed of the vehicle.Furthermore, the main radiator may receive the airflow through the grillwhich may affect the value of Qrad_(main) _(amb) . In that regard, thevalues of Q_(rad) _(sub1) , Q_(rad) _(sub2) , and Qrad_(main) _(amb) maybe based on an amount of airflow received via the grill (which is basedon a speed of the vehicle), a temperature of the airflow, and an amountof the fluid that flows through each of the radiators. Therefore, theECU may receive the vehicle speed and may calculate the values ofQ_(rad) _(sub1) , Q_(rad) _(sub2) , and Qrad_(main) _(amb) based on thereceived vehicle speed. The ECU may further estimate the temperature ofthe ambient air based on a temperature sensor located in or on thevehicle.

In block 822, the ECU may calculate a desired fan speed of the fan toachieve the desired amount of thermal energy to be removed from the mainradiator by the fan. The ECU may calculate the desired fan speed usingan equation similar to equation 6 below.

$\begin{matrix}{{kf}_{{rad}_{{main}_{fan}}} = \frac{{Qrad}_{{main}_{fan}}}{\left( {{Trad}_{main} - {{Tair}\_ {in}}} \right)}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

In equation 6,

kf_(rad_(main_(fan)))

represents a radiator heat transfer coefficient. This coefficient is afunction of the flow rate of the fluid and a speed of the air throughthe radiator, and may be determined experimentally. This coefficient maybe used (along with a current flow rate of the fluid) to solve for anangular velocity of the fan (i.e., fan speed), which corresponds to adesirable voltage level of the fan. Qrad_(main) _(fan) represents thedesired amount of thermal energy to be removed from the main radiator bythe fan that was calculated in block 820. Trad_(main) represents atemperature of the fluid at a fluid inlet of the main radiator and maybe received from the state estimator in block 804. Tair_in represents atemperature of the air at an air inlet of the main radiator and maylikewise be received from the state estimator in block 804.

After calculating the radiator heat transfer coefficient, the ECU maythen determine a desired fan speed. The ECU may determine the desiredfan speed using a lookup table. In particular, the ECU may compare theradiator heat transfer coefficient to a lookup table and retrieve acorresponding desired fan speed.

In some embodiments, the ECU may determine the desired fan speed basedon a function of the radiator heat transfer coefficient and a volumetricflow rate of the fluid through an inlet of the main radiator. In someembodiments, the ECU may compare the result of the function to a lookuptable and retrieve the desired fan speed based on the comparison.

In block 824, the ECU may determine a desirable power signal to provideto the fan. The desirable power signal may be based on one or both ofthe radiator heat transfer coefficient or the desired fan speed. Forexample, the ECU may compare the desired fan speed to a lookup table andretrieve a corresponding desirable power signal to provide to the fan.In some embodiments, the desirable power signal may correspond to adirect current (DC) power signal having a specific voltage. In someembodiments, the desirable power signal may correspond to an alternatingcurrent (AC) power signal having a specific root mean square (RMS)voltage or a specific duty cycle. In that regard, the desirable powersignal may include one or more of a specific voltage (DC or RMS) or aspecific duty cycle of the power signal.

In block 826, the ECU may provide the desirable power signal to the fanto cause the fan to operate at the desired speed to blow air towards themain radiator at the desirable speed of the air.

In some embodiments, the ECU may control the fan of the radiator in adifferent manner than that shown in blocks 818 to 826. In particular,the ECU may compare a radiator outlet temperature, corresponding to thetemperature of the fluid at the outlet of the radiator, to a target fuelcell inlet temperature. For example, the ECU may determine whether theradiator outlet temperature is greater than or equal to a sum of thetarget fuel cell inlet temperature and a threshold temperature, such as3 degrees C., 5 degrees C., 7 degrees C., or the like. If the radiatoroutlet temperature is greater than or equal to the sum, then the ECU mayinitiate a fan-on event. When the radiator outlet temperature becomesless than the sum, then the ECU may cancel the fan-on event. The ECU maycontrol the fan to turn on when the fan-on event is initialized, and toturn off when the fan-on event is cancelled.

In some embodiments, the ECU may latch the fan-on event. For example,the ECU may control the fan-on event to remain in place for apredetermined period of time after initiating the fan-on event andbefore cancelling the fan-on event. The predetermined period of time maycorrespond to a sufficient time period to reduce the likelihood of thefan oscillating between an “on” state and an “off” state frequentlyenough to irritate a driver. In that regard, the latching may reduce thelikelihood of the fan oscillating between “on” and “off,” which may beundesirable.

In some embodiments, the ECU may latch the fan-on event by adjusting thethreshold temperature based on whether the ECU is initiating the fan-onevent or is cancelling the fan-on event. For example, the ECU may setthe threshold temperature to be 6 degrees C. when initiating the fan-onevent, and may set the threshold temperature to be 8 degrees C. whencancelling the fan-on event. In that regard, the ECU may initiate thefan-on event when the temperature reaches a first value, such as 48degrees C., and may cancel the fan-on event when the temperature reachesa second value, such as 46 degrees C.

Referring now to FIGS. 9A and 9B, a method 900 for heating or cooling afuel cell circuit by estimating current conditions of the fuel cellcircuit is shown. The method may be performed, for example, by a stateestimator of an ECU such as the state estimator 320 of the ECU 102 ofFIG. 3.

In block 902, a model of the fuel cell circuit may be created andstored. The model may be created by designers of the fuel cell circuitand may be stored in a memory of the vehicle that is accessible by theECU. The ECU may use the model of the fuel cell circuit to estimatevarious temperatures, pressures, and the like throughout the variouscomponents of the fuel cell circuit.

Referring briefly to FIG. 10, a model 1000 of a fuel cell circuit, suchas the fuel cell circuit 118 of FIG. 2, is shown. The model 1000 mayinclude representations of the main components 1002 (represented bylarge squares), representations of pipes 1004 (represented by smallsquares) that connect the main components 1002, and representation offlow splitters 1006 (represented by triangles) in which the flow offluid is split into two or more flows.

Returning reference to FIGS. 9A and 9B, the ECU may receive a pluralityof inputs in block 904. The inputs may include detected temperaturevalues including temperatures detected by temperature sensors along withactuator control signals. The actuator control signals may correspond tocommanded actuator values of the actuators (including a pump, athree-way valve, and a radiator fan).

In block 906, the ECU may determine a temperature control signal thatcorresponds to a desired temperature of the fluid. For example, thetemperature control signal may correspond to a temperature rate ofchange determined by a state governor.

In block 908, the ECU may calculate flow resistance values of componentsof the fuel cell circuit, and in block 910 the ECU may calculate massflow values of the fluid through the components of the fuel cellcircuit. The flow resistance values and the mass flow values may becalculated for each component including the main components and pipes.

The flow resistance value for each component may be calculated using anequation similar to equation 7 below.

$\begin{matrix}{Z = \frac{{Fd}\left( {{Length} + {Length}_{Add}} \right)}{4{DA}^{2}\rho}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

In equation 7, Z represents the flow resistance. Fd corresponds to aDarcy friction factor of the component, which may be calculated fromexperimental correlations corresponding to the relevant flow regime(such as whether the flow is turbulent, laminar, etc.), which may bedictated by a corresponding Reynolds number. The Darcy friction factormay indicate an amount of friction loss through the component. Lengthrepresents a length of the component. Length_(add) corresponds to atuning parameter which may be adjusted by the ECU during operation ofthe fuel cell circuit, or by designers of the ECU, to increase inaccuracy of the calculation for the flow resistance. The Length_(add)parameter may be adjusted until the flow resistance curve issubstantially equal to an empirical curve. D represents a hydraulicdiameter of the component, and A represents a cross-sectional area ofthe component. ρ represents density of the fluid within the component.In equation 7, Fd and ρ are variable parameters, and the remainingparameters remain constant over time.

The mass flow for a given component may be calculated using an equationsimilar to equation 2 described above.

Referring again to FIG. 10, due to the law of conservation of mass, massflow of the fluid through components connected adjacently in series willbe the same. For example, a fuel cell stack 1008 and a pipe 1010 areconnected in series. Thus, all of the fluid that flows through the fuelcell stack 1008 will subsequently flow through the pipe 1010 withoutbecoming separated. In that regard, the mass flow of the fluid throughthe fuel cell stack 1008 will be equal to the mass flow of the fluidthrough the pipe 1010. Similarly, the mass flow of the fluid through anintercooler 1012 will be equal to the mass flow of the fluid throughanother pipe 1014.

When fluid from multiple components join together, such as at a junction1016, the mass flow after the junction (i.e., through a subsequentcomponent, such as a pipe 1018) will be equal to a sum of the mass flowthrough the components. In that regard, the mass flow of the fluidthrough the pipe 1018 will be equal to a sum of the mass flow throughthe first pipe 1010 and the mass flow through the second pipe 1014.

The calculation for mass flow, however, becomes more challenging forlocations in which the flow of the fluid is split (i.e., wherecomponents are connected in parallel). For example and referring toFIGS. 10 and 11, a diagram 1100 illustrates an exemplary flow splittingsituation. The diagram 1100 includes a main flow path 1102 that splitsinto a first flow path 1104 and a second flow path 1106 at a flowsplitter 1108. The first flow path 1104 flows through a first component1110 and a second component 1112 before rejoining with the second flowpath 1106 at a junction 1114. The second flow path 1106 flows through athird component 1116 and a fourth component 1118 before rejoining withthe first flow path 1104 at the junction 1114.

The diagram 1100 may loosely represent a portion of the model 1000including a flow splitter 1020 (represented by the flow splitter 1108),a first flow path 1022 and a second flow path 1024. The first flow path1022 includes two pipes 1026, 1028 and a main radiator 1030, and thesecond flow path 1024 includes two pipes 1032, 1034 and a secondaryradiator 1036. As shown, the model 1000 of the fuel cell circuitincludes multiple compound flow splits and parallel branches thatinclude multiple components connected in series.

When solving for the mass flows and flow resistances of the model 1000,the flow resistances of one or more component may be known, and the massflow may be known for at least one component (such as a pump 1038).Because the mass flow is known for one component the mass flow willremain the same for each subsequent component before reaching a flowsplitter. In that regard, the mass flow of the fluid through anotherpipe 1040 will be equal to the mass flow of the fluid through the pump1038.

When the fluid reaches a flow splitter, additional calculations may beperformed to calculate equivalent flow resistances of combinations ofcomponents as well as mass flows through each branch. The mass flow({dot over (m)}_(total)) of the main flow path 1102 may be known (i.e.,it may be set to be equal to the mass flow through a previous seriescomponent). Likewise, flow resistances of the components 1110, 1112,1116, 1118 may be known.

In order to calculate equivalent flow resistances, equations 8 and 9below may be used.

$\begin{matrix}{Z_{{eq}\mspace{11mu} {series}} = {Z_{1} + Z_{2}}} & {{Equation}\mspace{14mu} 8} \\{Z_{{eq}\mspace{11mu} p\; {arallel}} = \frac{z_{4}}{\left( {1 + \sqrt{\frac{z_{3}}{z_{4}}}} \right)^{2}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

Equation 8 may be used to calculate equivalent flow resistance forcomponents connected in series. In that regard, an equivalent flowresistance through the first flow path 1104 may be equal to a sum of theflow resistance (Z₁) of the first component 1110 and the flow resistance(Z₂) of the second component 1112.

Equation 9 may be used to calculate equivalent flow resistance forcomponents connected in parallel. For example, the equivalent flowresistance through the first flow path 1104 (Z₃) and through the secondflow path 1106 (Z₄) may be known. In that regard, an equivalent flowresistance corresponding to a flow resistance through all of thecomponents 1110, 1112, 1116, 1118 may be calculated using equation 9.

In order to calculate mass flow ({dot over (m)}₁) through the first flowpath 1104 and mass flow ({dot over (m)}₂) through the second flow path1106, equations 10 and 11 below may be used.

$\begin{matrix}{{\overset{.}{m}}_{1} = \frac{{\overset{.}{m}}_{total}}{1 + \sqrt{\frac{z_{3}}{z_{4}}}}} & {{Equation}\mspace{14mu} 10} \\{{\overset{.}{m}}_{2} = {{\overset{.}{m}}_{total} - {\overset{.}{m}}_{1}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Equation 10 may be calculated to determine the mass flow ({dot over(m)}₁) of the fluid through the first flow path 1104. Z₃ represents theequivalent flow resistance of the components 1110, 1112 of the firstflow path 1104, and Z₄ represents the equivalent flow resistance of thecomponents 1116, 1118 of the second flow path 1106. However, Z₃ and Z₄are unknown values at the current timestep. In that regard, equation 10is to be solved using Z₃ and Z₄ from a previous time period. Becausecalculations are performed at relatively short intervals (such asbetween 1 millisecond (ms) and 1 second, or between 5 ms and 50 ms, orabout 16 ms), the equivalent flow resistances are unlikely tosignificantly vary between subsequent time periods. In that regard,solving equation 10 using the equivalent flow resistances from aprevious time period is likely to provide a relatively accurate massflow value. It is desirable to use the equivalent flow resistances fromthe previous timestep due to the fact that neither the current flowresistances nor the current mass flow values are known, and the factthat a mass flow value is necessary to solve for equivalent flowresistance (and vice versa, per Equation 7). Using the equivalent flowresistances from the previous timestep provides the advantage ofallowing the ECU to dynamically solve for the flow split in any branchin real time. In some embodiments, a tool called a “real time iterativesolver” may be used to solve the set of equations in real time.

Once the mass flow ({dot over (m)}₁) through the first flow path 1104 iscalculated using equation 10, the mass flow ({dot over (m)}₂) throughthe second flow path 1106 may be calculated using equation 11 bysubtracting the mass flow ({dot over (m)}₁) through the first flow path1104 from the total mass flow ({dot over (m)}_(total)).

After calculating the mass flow values, equations 8 through 11 may becalculated again to determine flow resistances for the current timeperiod. These calculations may be made using the mass flow valuescalculated based on the flow resistances of the previous time period.

Returning reference to FIGS. 9A, 9B, and 10, the ECU may determine areservoir pressure of fluid within a reservoir 1042 of the fuel cellcircuit in block 912. The reservoir 1042 may be a reservoir thatcontains fluid to be added to the fuel cell circuit. In someembodiments, the reservoir 1042 may include a port that allows a user ofa corresponding vehicle to provide the fluid, such as a coolant. Thereservoir pressure may be determined based on sensor data or may becalculated by the ECU.

In block 914, the ECU may calculate pressure values for each of thecomponents of the fuel cell circuit based on the reservoir pressure andthe mass flow values calculated in block 910. In particular, a pressuredrop across each component of the fuel cell circuit may be calculatedusing equation 12 below.

ΔP={dot over (m)} ² Z  Equation 12:

In equation 12, ΔP represents the pressure drop over a given component,such as the pipe 1040. {dot over (m)} represents the mass flow of thefluid through the given component, and Z represents the flow resistanceof the component. In that regard, equation 12 may be used to calculatethe pressure drop over each component of the fuel cell circuit.

The pump 1038 may operate as both a pressure source and a mass flowsource. In some embodiments, the pump 1038 may be a turbo style pump,meaning that the pump speed, mass flow through the pump 1038, andpressure values are coupled. Thus, a previous timestep total systempressure drop value may be used, along with a current timestep pumpspeed, to calculate or estimate a current timestep total mass flow(i.e., mass flow through the pump 1038).

After the reservoir pressure and the pressure drop over each componentof the fuel cell circuit are known, the pressures at the inlets andoutlets of each component may be calculated. For example, the pressureat an outlet of a pipe 1044 is equal to the reservoir pressure becausethe outlet of the pipe 1044 and the reservoir 1042 are directlyconnected. Because the pressure drop over the pipe 1044 is known, thepressure at the inlet of the pipe 1044 may be calculated by adding thepressure drop over the pipe 1044 to the reservoir pressure. Thiscalculation may continue around the fuel cell circuit until the pressureat each node of the fuel cell circuit is determined.

In block 916, density values of the fluid through each of the componentsmay be calculated. For example, the density values may be calculatedusing an equation similar to equation 7 above.

In block 918, specific heat values may be calculated for the fluid ineach of the components. For example, the specific heat values may becalculated using an equation similar to equation 2 above.

In block 920, heat transfer values may be calculated for each of thecomponents of the fuel cell circuit. The heat transfer values maycorrespond to an amount of heat that is added to, or subtracted from,the fluid by the given component. As described above, the intercooler1012 and the fuel cell stack 1008 are the two components which add heatto the fluid. The heat transfer value (Q_(FC)) of the fuel cell stack1008 may be calculated or estimated using an equation, such as equation2 above. The heat transfer value of the intercooler 1012 may becalculated using a similar or other equation.

The radiators 1046 and each of the pipes 1004 may each remove heat fromthe fluid. The heat transfer value of each of the radiators 1046 of thefuel cell circuit may be calculated using equations, such as equations 3through 6 described above. The heat transfer value of each of the pipes1004 may be estimated based on the convection properties of the pipes1004, the temperature of the fluid, and the ambient temperature outsideof the pipes 1004.

In block 922, the ECU may calculate a plurality of temperature valuescorresponding to the components of the fuel cell circuit. For example,the ECU may calculate temperature values at the outlets of thecomponents. Due to the conservation of energy laws, a temperature at anoutlet of the first component will be equal to a temperature at an inletof an adjacent downstream component. The temperature values may becalculated using a temperature value from a previous time period. Thetemperature values may be calculated using an equation similar toequation 13 below.

$\begin{matrix}{T_{k + 1} = {x_{k + 1} - {e^{\frac{- {\Delta t}}{\tau}}\left\lbrack {x_{k + 1} - T_{k}} \right\rbrack}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

In equation 13, T_(k+1) represents the temperature of the fluid at anoutlet of the corresponding component at a current time period. T_(k)represents the temperature of the fluid at a previous time period whichmay have been previously calculated. Δt represents a length of the timeperiod (such as between 1 ms and 1 second, or between 5 ms and 50 ms, orabout 16 ms). τ represents a time constant and is equal to

$\frac{\rho V}{m},$

where ρ represents density of the fluid within the component, Vrepresents volume of the fluid within the component, and m, representsmass flow of the fluid through the component. x_(k+1) represents anindependent variable, the value of which is calculated for the currenttime period.

In particular, x_(k+1) may be provided as

$\left\lbrack {T_{1} + {\frac{1}{\rho C}\left( {P_{1} - P_{2}} \right)} - {\frac{1}{c\overset{.}{m}}(Q)}} \right\rbrack.$

T₁ represents a temperature at an inlet of the component. ρ representsdensity of the fluid within the component, and c represents specificheat of the fluid within the component. P₁ represents a pressure of thefluid at an inlet of the component, and P₂ represents a pressure of thefluid at an outlet of the component. Tit represents mass flow of thefluid through the component. Q represents the heat transfer value of thecomponent and may be obtained from the calculation performed in block920.

Equation 13 may be performed by the ECU at each time period for each ofthe components. Because the temperature is known (from temperaturesensors) for at least one component of the fuel cell circuit (such as anoutlet of the fuel cell stack 1008), this temperature may be used as aninput for solving an outlet temperature of an adjacent downstreamcomponent (such as an inlet temperature of the pipe 1010). Once theoutlet temperature of the adjacent downstream component is calculated,the outlet temperature may be computed or calculated for the nextcomponent, and so forth, until the outlet temperature is known for eachcomponent of the fuel cell circuit.

In block 924, the ECU may calculate a desired actuator position of eachactuator of the fuel cell circuit. As described above, the actuators mayinclude a radiator fan, a pump, and a three-way valve. For example, afeedforward control or a feedback control of the ECU may calculate thedesired actuator positions based on the temperature control signal andthe values calculated by the state estimator, such as the mass flowvalues, the pressure values, and the temperature values.

In block 926, the ECU may control the actuators to have the desiredactuator position.

Referring now to FIGS. 12A and 12B, a method 1200 for feedback basedheating or cooling of a fuel cell circuit is shown. The method 1200 maybe performed by a feedback control, such as the feedback control 316 ofFIG. 3.

In block 1202, the ECU may determine a temperature control signalcorresponding to a desired temperature of the fluid in the fuel cellcircuit. For example, the temperature control signal may correspond to adesired temperature of the fluid and may include, for example, atemperature rate of change. In some embodiments, the temperature controlsignal may be determined based on a desired temperature of the fluid atone or more location. The temperature control signal may be determinedusing a state governor such as the state governor 308 of FIG. 3.

In block 1204, the ECU may perform a feedforward control of the actuatorin order to increase or decrease the fluid temperature based on thetemperature control signal. For example, the ECU may determine afeedforward control signal using a feedforward control such as thefeedforward control 312 of FIG. 3. The feedforward control may be basedon the temperature control signal and estimated values that werecalculated using a state estimator. In some embodiments, the ECU maydirectly control one or more actuator of the fuel cell circuit using thefeedforward control. In some embodiments, the ECU may directly controlone or more actuator using a combination of the feedforward control andfeedback control.

In block 1206, the fluid temperature of the fluid at one or morelocation may be detected by a temperature sensor or calculated by theECU, such as in a state estimator.

In block 1208, the ECU may determine a temperature difference betweenthe detected or calculated fluid temperature and a desired temperatureof the fluid at one or more location. For example, the ECU may determinea temperature difference between a detected or calculated temperature atan outlet of the fuel cell stack and a desired temperature of the fluidat the outlet of the fuel cell stack.

In block 1210, the ECU may determine or calculate a sensitivity. Thesensitivity may correspond or associate a change in actuator position(including a physical change in actuator position, a change in anactuator control signal, or a change in parameter value used todetermine the actuator control signal) to a change in the fluidtemperature. For example, the sensitivity may indicate how much changein an actuator position of an actuator changes the fluid temperature ofthe fluid by 1 degree. As another example, the sensitivity may indicatehow much a change in mass flow changes the fluid temperature of thefluid by 1 degree.

In some embodiments and in block 1212, the ECU may divide thesensitivity by a time delay. This may be especially useful if the fluidtemperature of the fluid is detected by a sensor. This is because thefluid temperature detected by a sensor may be delayed by one or moreseconds, such as 1 to 5 seconds. In that regard, if control of theactuator is based on a time delayed sensor reading, the actuator controlmay oscillate due to the delayed reading. Dividing the sensitivity bythe time delay results in a more gradual change in the actuator control,thus reducing the likelihood of oscillation of the actuator control.

In some embodiments, especially if the fluid temperature is calculatedby the ECU rather than detected by a sensor having a time delay, block1212 may be avoided. This is because the calculation of the fluidtemperature may have a relatively small delay, if any delay at all.Therefore, the actuator control may be based on a more current readingsuch that the time delay operation is unnecessary.

The temperature difference determined in block 1208 may correspond to atemperature error. Stated differently, the temperature differencecorresponds to an error because it is the difference between a desiredtemperature at the location and the actual temperature at the location.In that regard and in block 1214, the sensitivity may be applied to thetemperature difference in order to determine an error signal. The errorsignal may correspond to, or indicate, an error in the actuator positionor an error in the parameter used to calculate the actuator positionthat caused the temperature difference. For example, the error signalmay indicate that a pump is pumping the fluid through the fuel cellcircuit at a mass flow rate that is either too low or too high. Theerror signal may further indicate or correspond to a difference in massflow that will cause the actual temperature of the fluid to berelatively equal to the desired temperature of the fluid.

In block 1216, the ECU may pass the error signal through aproportional-integral-derivative (PID, or PI) controller to generate afeedback control signal. The PID controller may analyze past and presentvalues of the error signal and generate the feedback control signalbased on present error values, past error values, and potential futureerrors of the error signal.

In block 1218, the ECU may control the actuator based on the feedbackcontrol signal. For example, the ECU may generate a sum of thefeedforward control signal (such as a control signal generated using themethod 800 of FIGS. 8A and 8B) and the feedback control signal andcontrol the actuator based on the sum. In some embodiments, the ECU maycontrol the actuator based on the feedback control signal alone.

Referring now to FIG. 13, the ECU 102 of FIG. 2, and in particular thefeedback control 316, may include a three-way valve controller 1300. Thethree-way valve controller 1300 may include logic or dedicated hardwaredesigned to perform a method similar to the method 1200 of FIGS. 12A and12B to perform feedback control of the three-way valve.

The three-way valve controller 1300 may include a difference block 1302.The difference block 1302 may receive a fluid temperature 1304 measuredor calculated at the inlet of the fuel cell stack. For example, thefluid temperature 1304 may be calculated by a state estimator of the ECU102. The difference block 1302 may further receive a desired temperature1306 corresponding to a desired temperature of the fluid at the inlet ofthe fuel cell stack. The difference block 1302 may output a temperaturedifference 1308 corresponding to a difference between the fluidtemperature 1304 and the desired temperature 1306.

The three-way valve controller 1300 may further include a seconddifference block 1310. The second difference block 1310 may receive aradiator temperature 1312 corresponding to a temperature of the fluid atthe outlet of the radiator. The second difference block 1310 may furtherreceive a bypass fluid temperature 1314 corresponding to a temperatureof the fluid at a location along a bypass branch of the fuel cellcircuit. The second difference block 1310 may output a difference 1316between the radiator temperature 1312 and the bypass fluid temperature1314.

The three-way valve controller 1300 may further include a sensitivityblock 1318. The sensitivity block 1318 may receive the difference 1316between the radiator temperature 1312 and the bypass fluid temperature1314 along with a pump fluid temperature 1320 corresponding to atemperature of the fluid at an inlet of the pump. The sensitivity block1318 may determine a sensitivity 1322 that corresponds a change in valveposition of the three-way valve to a change in fluid temperature of thefluid, such as a fluid temperature at the inlet of the fuel cell stack.For example, the sensitivity 1322 may indicate how much of a change invalve position (Z) results in a 1 degree change of the fluid temperatureat the inlet of the fuel cell stack.

The sensitivity 1322 may be calculated using an equation similar toequation 14 below. In some embodiments, the sensitivity may be providedas a lookup table or lookup map that is populated using an equationsimilar to equation 14. In some embodiments, the sensitivity may beprovided, as the equation such that the sensitivity block 1318calculates the sensitivity based on the received inputs.

$\begin{matrix}{\frac{dZ}{dT} = \frac{\left( \frac{\left( {\left( {T_{{pump}\mspace{14mu} {in}} + {\Delta T}_{({1C})}} \right) - T_{bypass}} \right)}{\left( {T_{{rad}\mspace{14mu} {out}} - T_{bypass}} \right)} \right) - \left( \frac{\left( {T_{{pump}\mspace{14mu} {in}} - T_{bypass}} \right)}{\left( {T_{{rad}\mspace{14mu} {out}} - T_{bypass}} \right)} \right)}{{\Delta T}_{({1C})}}} & {{Equation}\mspace{14mu} 14}\end{matrix}$

In equation 14,

$\frac{dZ}{dT}$

represents the sensitivity 1322 that is determined or calculated by thesensitivity block 1318. T_(pump in) represents the pump fluidtemperature 1320. ΔT represents a set change in the fluid temperature atthe inlet of the fuel cell stack. In some embodiments, ΔT is set to beequal to 1 degree C. T_(bypass) represents the bypass fluid temperature1314, and T_(rad out) represents the radiator temperature 1312 at theoutlet of the radiator. The sensitivity

$\frac{dZ}{dT}$

indicates how much the fluid split ratio of the three-way valve mustchange in order to achieve a predefined temperature change (such as 1degree C.) of the fluid at the inlet of the fuel cell stack.

As described above with reference to FIGS. 8A and 8B, the fluid splitratio may correspond to a ratio of an amount of fluid (e.g., measuredusing mass flow) that is directed towards the radiators to a totalamount of fluid (e.g., measured using mass flow) flowing through theentire fuel cell circuit. Thus, a fluid split ratio of 1 may indicatethat all of the fluid is flowing through the radiators and none throughthe bypass branch. Furthermore and also as described above withreference to FIGS. 8A and 8B, the fluid split ratio of the three-wayvalve (Z) is a function of a difference between the radiator temperature1312 at the outlet of the radiator and the bypass fluid temperature1314.

The three-way valve controller 1300 may further include a multiplicationblock 1324. The multiplication block 1324 may apply the sensitivity 1322to the temperature difference 1308. For example, the multiplicationblock 1324 may multiply the temperature difference 1308 by thesensitivity 1322. The result of the multiplication block 1324 may be anerror signal 1326, and may indicate an error in the three-way valveposition (measured, for example, in values corresponding to the fluidsplit ratio).

The three-way valve controller 1300 may further include a proportionalintegral derivative (PID) controller 1328. The PID controller 1328 mayreceive the error signal 1326 and may generate a feedback control signal1330 by accounting for present error values, past error values, andpotential future errors of the error signal 1326.

The ECU 102 may further include a combination block 1332 that receivesthe feedback control signal 1330 along with a feedforward control signal1334. The feedforward control signal 1334 may correspond to afeedforward control of the three-way valve as determined or calculatedby a feedforward control such as the feedforward control 312 of FIG. 3.

The combination block 1332 may generate a sum of the feedback controlsignal 1330 and the feedforward control signal 1334. The combinationblock 1332 may output a combined control signal 1336 that corresponds toa final desired valve position based on feedforward and feedbackcontrol. In particular, the combined control signal 1336 may correspondto a final desired fluid split ratio.

The combined control signal 1336 may be received by a lookup table 1338.In some embodiments, the lookup table 1338 may instead include acalculation or other method or apparatus for converting a fluid splitratio to a desired valve position. In that regard, the lookup table 1338may receive the combined control signal 1336, and may convert thecombined control signal 1336 into a final desired valve position 1340,and may output the final desired valve position 1340. The ECU maycontrol the three-way valve based on the final desired valve position1340.

Referring now to FIG. 14, the ECU 102 of FIG. 2, and in particular thefeedback control 316, may include a pump controller 1400. The pumpcontroller 1400 may be implemented as logic or dedicated hardware anddesigned to perform a method similar to the method 1200 of FIGS. 12A and12B to perform feedback control of the pump.

The pump controller 1400 may include a difference block 1402. Thedifference block 1402 may receive a fluid temperature 1404 measured orcalculated at the outlet of the fuel cell stack. For example, the fluidtemperature 1404 may be measured by a temperature sensor, such as thetemperature sensor 224 of FIG. 2, or may be calculated by a stateestimator of the ECU 102. The difference block 1402 may further receivea desired temperature 1406 corresponding to a desired temperature of thefluid at the outlet of the fuel cell stack. For example, the desiredtemperature 1406 may correspond to a commanded temperature of the fluidat the outlet of the fuel cell stack and may be determined by an uppercontroller of the ECU 102. The difference block 1402 may output atemperature difference 1408 corresponding to a difference between thefluid temperature 1404 and the desired temperature 1406.

The pump controller 1400 may further include a second difference block1410. The second difference block 1410 may receive the fluid temperature1404 and a fuel cell inlet temperature 1414 corresponding to atemperature of the fluid at the inlet of the fuel cell stack. The fuelcell inlet temperature 1414 may be measured or calculated by a stateestimator of the ECU 102. The second difference block 1410 may output adifference 1416 between the fluid temperature 1404 and the fuel cellinlet temperature 1414. The difference 1416 may also be referred to as atemperature gradient of the fuel cell stack as it corresponds to atemperature difference between the inlet and the outlet of the fuel cellstack.

The pump controller 1400 may further include a sensitivity block 1418.The sensitivity block 1418 may receive the difference 1416 along with anamount of heat 1420 output by the fuel cell stack (corresponding to anamount of heat transferred from the fuel cell stack to the fluid) and anequivalent specific heat 1412 of the fluid in the fuel cell stack. Thesensitivity block 1418 may determine a sensitivity 1422 that correspondsa change in pump output (such as a change in mass flow of the fluid) ofthe pump to a change in fluid temperature of the fluid, such as a fluidtemperature at the outlet of the fuel cell stack. For example, thesensitivity 1322 may indicate how much of a change in mass flow outputby the pump corresponds to a 1 degree change of the fluid temperature atthe outlet of the fuel cell stack.

The sensitivity 1422 may be calculated using an equation similar toequation 15 below. In some embodiments, the sensitivity may be providedas a lookup table or lookup map that is populated using an equationsimilar to equation 15. In some embodiments, the sensitivity may beprovided as the equation such that the sensitivity block 1418 calculatesthe sensitivity based on the received inputs.

$\begin{matrix}{\frac{\Delta \overset{.}{m}}{{dT}_{{FC}\mspace{14mu} {out}}} = \frac{\frac{- Q_{FC}}{C_{eq}\left( {{- \left( {T_{{FC}\mspace{14mu} {out}} - T_{{FC}\mspace{14mu} {in}}} \right)} + {dT}_{{FC}\mspace{14mu} {out}}} \right)} - \frac{- Q_{FC}}{C_{eq}\left( {- \left( {T_{{FC}\mspace{14mu} {out}} - T_{{FC}\mspace{14mu} {in}}} \right)} \right)}}{{dT}_{{FC}\mspace{14mu} {out}}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

In equation 15,

$\frac{\Delta \overset{.}{m}}{{dT}_{{FC}\mspace{14mu} {out}}}$

represents the sensitivity 1422 that is determined or calculated by thesensitivity block 1418. As shown, the sensitivity 1422 corresponds achange in mass flow output by the pump (Δ{dot over (m)}) to a change ofthe fluid temperature at the outlet of the fuel cell stack(dT_(FC out)). In particular, the sensitivity

$\frac{\Delta \overset{.}{m}}{{dT}_{{FC}\mspace{14mu} {out}}}$

indicates an amount of change of the mass flow output by the pumprequired to achieve a predefined temperature change (such as 1 degreeC.). In some embodiments, dT_(FC out) is set to be equal to 1 degree C.c_(eq) represents an equivalent specific heat 1412 of the fluid in thefuel cell stack. Q_(FC) represents the amount of heat 1420 output by thefuel cell stack. T_(FC out) represents the fluid temperature 1404 of thefluid at the outlet of the fuel cell stack, and T_(FC in) represents thefuel cell inlet temperature 1414 at the inlet of the fuel cell stack.

The pump controller 1400 may further include a division block 1426. Thedivision block 1426 may receive the sensitivity 1422 along with a timedelay 1424. The division block 1426 may divide the sensitivity 1422 bythe time delay 1424. By performing this division, the division block1426 reduces the sensitivity 1422 to cause a more gradual change in thepump control. In that regard, the division block 1426 may reduceoscillation of the pump control. This may be useful if the fluidtemperature 1406 is detected by a temperature sensor due to the delayedreading of the temperature sensor. In some embodiments, the divisionblock 1426 may be excluded, particularly if the fluid temperature 1406is calculated by a state estimator of the ECU 102. The division block1426 may output an adjusted sensitivity 1428. In some embodiments, thethree-way valve controller 1300 of FIG. 13 may likewise include asimilar division block.

The pump controller 1400 may further include a multiplication block1430. The multiplication block 1430 may apply the adjusted sensitivity1428 to the temperature difference 1408. For example, the multiplicationblock 1430 may multiply the temperature difference 1408 by the adjustedsensitivity 1428. The result of the multiplication block 1430 may be anerror signal 1432, indicating an error in the desired mass flow to beoutput by the pump. In that regard, the error signal may include a massflow value.

The pump controller 1400 may further include a PID controller 1434. ThePID controller 1434 may receive the error signal 1432 and may generate afeedback control signal 1436 by accounting for present error values,past error values, and potential future errors of the error signal 1432.

The ECU 102 may further include a combination block 1438 that receivesthe feedback control signal 1436 along with a feedforward control signal1440. The feedforward control signal 1448 may correspond to afeedforward control of the pump as determined or calculated by afeedforward control such as the feedforward control 312 of FIG. 3.

The combination block 1438 may generate a sum of the feedback controlsignal 1436 and the feedforward control signal 1440. The combinationblock 1438 may output a combined control signal 1442 that corresponds toa final desired mass flow to be output by the pump based on feedforwardand feedback control.

The combined control signal 1442 may be received by a lookup table 1444.In some embodiments, the lookup table 1444 may instead include acalculation or other method or apparatus for converting a mass flow rateto a pump control signal. In that regard, the lookup table 1444 mayreceive the combined control signal 1442, and may convert the combinedcontrol signal 1442 into a final pump control signal 1446. The ECU maycontrol the pump based on the final pump control signal 1446.

Referring now to FIGS. 15A and 15B, a method 1500 for correcting anestimated parameter is shown. The method 1500 may be performed bycomponents of a fuel cell circuit such as the fuel cell circuit 118 ofFIG. 2. For example, the method 1500 may be performed by an observer ofan ECU, such as the observer 322 of FIG. 3. The estimated parameter mayinclude an estimated or calculated parameter generated by a stateestimator. Correction of the estimated parameter may cause multiplecalculations by the state estimator to improve in accuracy due to atrickle-down effect.

In block 1502, the ECU may estimate an estimated parameter that affectsan amount of heat removed by a radiator. As described above, a velocityof the ambient air that passes over the radiators may be included in acalculation for the amount of heat removed by the radiator. In thatregard, the estimated parameter may include the velocity of the ambientair that flows over one or more radiator. In some embodiments, theestimated parameter may include another value such as a temperature ofthe ambient air or the like.

In block 1504, the ECU may determine an actuator control signal used tocontrol the actuator. For example, the actuator may include the fan suchthat the control signal corresponds to a fan speed of the fan or a powersignal for powering the fan. The ECU may determine the actuator controlsignal in a feedforward control such as the feedforward control 312 ofFIG. 3.

In block 1506, a temperature sensor may detect a fluid temperature ofthe fluid within the fuel cell circuit. For example, the fluidtemperature may be detected at an outlet of one or more radiator, suchas by the temperature sensor 226 of the fuel cell circuit 118 of FIG. 2.

In block 1508, the ECU may estimate an estimated fluid temperature ofthe fluid. For example, the estimated fluid temperature may be estimatedfor the same location at which the fluid temperature was detected inblock 1506 (i.e., the outlet of the radiators). The ECU may estimate theestimated fluid temperature using a state estimator, such as the stateestimator 320 of FIG. 3.

In block 1510, the ECU may calculate or determine a temperaturedifference between the fluid temperature that was detected in block 1506and the estimated fluid temperature that was calculated in block 1508.In that regard, the temperature difference may indicate an error or amiscalculation by the state estimator as it represents a differencebetween the measured temperature and the temperature estimated by thestate estimator.

In block 1512, the ECU may determine or calculate a sensitivity. Thesensitivity may correspond or associate a change in the estimatedparameter to a change in the fluid temperature. Because the estimatedparameter is used to determine the control signal for the fan, a changein the estimated parameter ultimately affects an amount of heat removedfrom the fluid by the radiators. For example, the sensitivity mayindicate how much change in the estimated parameter is needed to causethe fluid temperature to change by 1 degree C. In some embodiments, thefluid temperature may be measured or calculated at the outlet of theradiators.

In block 1514, the ECU may apply the sensitivity to the temperaturedifference in order to determine an error signal. The error signal mayindicate, or correspond to, an error in the estimated parameter thatcaused the temperature difference. For example, the error signal mayindicate that the value of the estimated parameter (e.g., ambient airvelocity) calculated by the state estimator is too low or too high. Theerror signal may further indicate or correspond to a difference in thevalue of the estimated parameter that will cause the estimated fluidtemperature to be substantially equal to the actual fluid temperature ofthe fluid.

In block 1516, the ECU may pass the error signal through a PIDcontroller to generate an updated estimated parameter. The PIDcontroller may analyze past and present values of the error signal andgenerate the updated estimated parameter based on present error values,past error values, and potential future error values of the errorsignal.

In block 1518, the ECU may determine an updated actuator control signalbased on the updated estimated parameter. For example, the feedforwardcontrol may generate a new fan control signal using the updatedestimated parameter rather than the original estimated parametergenerated by the state estimator. In that regard, use of the updatedestimated parameter is likely to cause the actual temperature of thefluid to be closer in value to a desired temperature of the fluid.

In block 1520, the ECU may control the actuator based on the updatedactuator control signal generated in block 1518.

Referring now to FIG. 16, the ECU 102 of FIG. 2, and in particular theobserver 322, may include an estimated parameter controller 1600. Theestimated parameter controller 1600 may be implemented using logic ordedicated hardware and designed to perform a method similar to themethod 1500 of FIGS. 15A and 15B to update a parameter estimated by thestate estimator.

The estimated parameter controller 1600 may include a difference block1602. The difference block 1602 may receive a fluid temperature 1604measured at the outlet of the radiators (such as by the temperaturesensor 226 of FIG. 2). The difference block 1602 may further receive anestimated fluid temperature 1606 corresponding to a fluid temperature ofthe fluid at the outlet of the radiators that was calculated by a stateestimator. The difference block 1602 may output a temperature difference1608 corresponding to a difference between the measured fluidtemperature 1604 and the estimated fluid temperature 1606. In thatregard, the temperature difference 1608 may indicate an error in thecalculation of the estimated fluid temperature 1606.

The estimated parameter controller 1600 may further include asensitivity block 1614. The sensitivity block 1614 may receive the fluidtemperature 1604, a temperature 1610 of the ambient air flowing over theradiators, and a specific volumetric flowrate 1612 (e.g., measured inliters per minute) of the coolant (i.e., ambient air) flowing over theradiators. The temperature 1610 and the specific volumetric flowrate1612 may be estimated or calculated by a state estimator. Thesensitivity block 1614 may determine a sensitivity 1618 that correspondsa change in the velocity of the ambient air to a change in fluidtemperature of the fluid, such as the fluid temperature 1604 measured atthe outlet of the radiators. For example, the sensitivity 1618 mayindicate how much change in velocity will result in a 1 degree C. changeof the fluid temperature 1604.

The sensitivity 1618 may be calculated using an equation similar toequation 16 below. In some embodiments, the sensitivity may be providedas a lookup table or lookup map that is populated using an equationsimilar to equation 16. In some embodiments, the sensitivity may beprovided as the equation such that the sensitivity block 1614 calculatesthe sensitivity based on the received inputs.

$\begin{matrix}{\frac{dT}{dv} = \frac{\left( {{{Var}1} - {{Var}2}} \right)}{{\Delta v}_{({1{m/s}})}}} & {{Equation}\mspace{14mu} 16}\end{matrix}$

In equation 16,

$\frac{dT}{dv}$

represents the sensitivity 1618. As mentioned above, the sensitivity1618 may correspond a change in the velocity of ambient air to apredetermined change in temperature (such as 1 degree C.). Δν representsa predetermined change in the velocity, such as 1 meter per second (1m/s). Equation 1 illustrates that the sensitivity 1618 is a function ofa temperature of the fluid at the inlet of all radiators (Trad_(in)),the temperature 1610 of the ambient air flowing over all radiators(Tair_in), and the specific volumetric flowrate 1612 of the coolant(i.e., air) that flows over the corresponding radiator (

).

${{Var}1}\mspace{14mu} {may}\mspace{14mu} {be}\mspace{14mu} {represented}\mspace{14mu} {{as}\left( {{Trad}_{in} - \left( {\frac{\begin{pmatrix}{{{kf}\_ {MAP}}_{main}\left( {\left( v_{{amb}_{air} + {\Delta v}_{({1{m/s}})}} \right),\overset{.}{V_{{coolant}\mspace{14mu} {rad}_{main}}}} \right)} \\\left( {{Trad}_{{main}_{in}} - {{Tair}\_ {in}}_{main}} \right)\end{pmatrix}}{\left( {{\overset{.}{m}}_{main}c_{main}} \right)} + \frac{\begin{pmatrix}{{{kf}\_ {MAP}}_{{sub}\; 1}\left( {\left( v_{{amb}_{air} + {\Delta v}_{({1{m/s}})}} \right),\overset{.}{V_{{coolant}\mspace{14mu} {rad}_{{sub}\; 1}}}} \right)} \\\left( {{Trad}_{{sub}\; 1_{in}} - {{Tair}\_ {in}}_{{sub}\; 1}} \right)\end{pmatrix}}{\left( {{\overset{.}{m}}_{{sub}\; 1}c_{{sub}\; 1}} \right)} + \frac{\begin{pmatrix}{{{kf}\_ {MAP}}_{{sub}\; 2}\left( {\left( v_{{amb}_{air} + {\Delta v}_{({1{m/s}})}} \right),\overset{.}{V_{{coolant}\mspace{14mu} {rad}_{{sub}\; 2}}}} \right)} \\\left( {{Trad}_{{sub}\; 2_{in}} - {{Tair}\_ {in}}_{{sub}\; 2}} \right)\end{pmatrix}}{\left( {{\overset{.}{m}}_{{sub}\; 2}c_{{sub}\; 2}} \right)}} \right)} \right)}$

In Var1, Trad_(in) represents the fluid temperature at the inlet of allradiators. kf_MAP_(xx) represents a lookup table value that isdetermined using a corresponding kf factor for each of the radiators(one main radiator (main) and two secondary radiators (sub1 and sub2)).ν_(amb) _(air) represents the velocity of the ambient air.

represents a specific volumetric flowrate of the coolant (i.e., air)that flows over the corresponding radiator. Trad_(xx) _(in) represents atemperature of the fluid at the inlet of each corresponding radiator.Tair_in_(xx) represents a temperature of the air flowing over eachcorresponding radiator. {dot over (m)}_(xx) represents the mass flow ofthe fluid flowing through the corresponding radiator. c_(xx) representsa specific heat of the fluid flowing through the corresponding radiator.

${Var2}\mspace{14mu} {may}\mspace{14mu} {be}\mspace{14mu} {represented}\mspace{14mu} {{as}\left( {{Trad}_{in} - \left( {\frac{\left( {{{kf}\_ {MAP}}_{main}\left( {v_{{amb}_{air}},\overset{.}{V_{{coolant}\mspace{14mu} {rad}_{main}}}} \right)\left( {{Trad}_{{main}_{in}} - {{Tair}\_ {in}}_{main}} \right)} \right)}{\left( {{\overset{.}{m}}_{main}c_{main}} \right)} + \frac{\left( {{{kf}\_ {MAP}}_{{sub}\; 1}\left( {v_{{amb}_{air}},\overset{.}{V_{{coolant}\mspace{14mu} {rad}_{{sub}\; 1}}}} \right)\left( {{Trad}_{{sub}\; 1_{in}} - {{Tair}\_ {in}}_{{sub}\; 1}} \right)} \right)}{\left( {{\overset{.}{m}}_{sub1}c_{sub1}} \right)} + \frac{\left( {{{kf}\_ {MAP}}_{{sub}\; 2}\left( {v_{{amb}_{air}},\overset{.}{V_{{coolant}\mspace{14mu} {rad}_{{sub}\; 2}}}} \right)\left( {{Trad}_{{sub}\; 2_{in}} - {{Tair}\_ {in}}_{{sub}\; 2}} \right)} \right)}{\left( {{\overset{.}{m}}_{{sub}\; 2}c_{{sub}\; 2}} \right)}} \right)} \right)}$

The estimated parameter controller 1600 may further include amultiplication block 1620. The multiplication block 1620 may receive thesensitivity 1618 and the temperature difference 1608, and may apply thesensitivity 1618 to the temperature difference 1608. For example, themultiplication block 1620 may multiply or divide the temperaturedifference 1608 by the sensitivity 1618. The result of themultiplication block 1620 may be an error signal 1622, such as an errorin the estimated parameter (i.e., the velocity of the ambient air).

The estimated parameter controller 1600 may further include a PIDcontroller 1624. The PID controller 1624 may receive the error signal1622 and may generate an updated estimated parameter 1626. The PIDcontroller 1624 may generate the updated estimated parameter 1626 byaccounting for present error values, past error values, and potentialfuture errors of the error signal 1622. The ECU 102 may then transferthe updated estimated parameter 1626 to a feedforward control forcontrolling the fan of the fuel cell circuit.

Where used throughout the specification and the claims, “at least one ofA or B” includes “A” only, “B” only, or “A and B.” Exemplary embodimentsof the methods/systems have been disclosed in an illustrative style.Accordingly, the terminology employed throughout should be read in anon-limiting manner. Although minor modifications to the teachingsherein will occur to those well versed in the art, it shall beunderstood that what is intended to be circumscribed within the scope ofthe patent warranted hereon are all such embodiments that reasonablyfall within the scope of the advancement to the art hereby contributed,and that that scope shall not be restricted, except in light of theappended claims and their equivalents.

What is claimed is:
 1. A system for heating or cooling a fuel cell circuit of a vehicle comprising: a fuel cell stack having a plurality of fuel cells and configured to receive a fluid and to heat the fluid; an actuator having an actuator position and configured to increase or decrease a fluid temperature of the fluid; a pipe configured to facilitate flow of the fluid through the fuel cell circuit; a memory configured to store a model of the fuel cell circuit; and an electronic control unit (ECU) coupled to the actuator and the memory and configured to: calculate a plurality of mass flow values of the fluid each corresponding to a mass flow of the fluid through the fuel cell stack or the pipe based on a previously-determined mass flow value and the model of the fuel cell circuit, calculate a plurality of pressure values each corresponding to a pressure of the fluid at an inlet or an outlet of the fuel cell stack or the pipe based on the plurality of mass flow values and the model of the fuel cell circuit, and control the actuator position of the actuator to increase or decrease the fluid temperature based on at least one of the plurality of mass flow values and at least one of the plurality of pressure values.
 2. The system of claim 1 wherein the ECU is further configured to: determine a temperature control signal corresponding to a desired temperature of the fluid at a fuel cell inlet or a fuel cell outlet of the fuel cell stack; calculate a desired actuator position of the actuator based on the temperature control signal, at least one of the plurality of mass flow values and at least one of the plurality of pressure values; and control the actuator position to be equal to the desired actuator position.
 3. The system of claim 1 further comprising a flow splitter configured to split the fluid into a first fluid flow and a second fluid flow, wherein: the pipe includes a first pipe configured to receive the first fluid flow and a second pipe configured to receive the second fluid flow; and the ECU is further configured to calculate a first pipe mass flow of the first fluid flow through the first pipe and a second pipe mass flow of the second fluid flow through the second pipe based on previously-determined flow resistances of the first pipe and of the second pipe.
 4. The system of claim 1 further comprising a reservoir configured to store the fluid at a reservoir pressure, wherein the ECU is further configured to identify a current reservoir pressure of the fluid in the reservoir, and calculate the plurality of pressure values further based on the current reservoir pressure.
 5. The system of claim 1 wherein the ECU is further configured to: calculate a plurality of density values each corresponding to a density of the fluid through the fuel cell stack or the pipe; calculate a plurality of specific heat values each corresponding to a specific heat of the fluid through the fuel cell stack or the pipe; and control the actuator position further based on at least one of the plurality of density values and at least one of the plurality of specific heat values.
 6. The system of claim 1 wherein the ECU is further configured to calculate a plurality of temperature values each corresponding to a temperature of the fluid at the outlet of a pump or the fuel cell stack based on a previously-determined temperature value at the outlet and the model of the fuel cell circuit.
 7. The system of claim 1 wherein the ECU is further configured to calculate an amount of heat generated by the fuel cell stack and to control the actuator position further based on the amount of heat generated by the fuel cell stack.
 8. A system for heating or cooling a fuel cell circuit of a vehicle comprising: a fuel cell stack having a plurality of fuel cells and configured to receive a fluid and to heat the fluid; a pump configured to pump the fluid through the fuel cell circuit at a pump speed; a pipe configured to facilitate flow of the fluid through the fuel cell circuit; a memory configured to store a model of the fuel cell circuit; and an electronic control unit (ECU) coupled to the pump and the memory and configured to: calculate a plurality of mass flow values of the fluid each corresponding to a mass flow of the fluid through the fuel cell stack, the pump, or the pipe based on a previously-determined mass flow value and the model of the fuel cell circuit, calculate a plurality of pressure values each corresponding to a pressure of the fluid at an inlet or an outlet of the fuel cell stack, the pump, or the pipe based on the plurality of mass flow values and the model of the fuel cell circuit, and control the pump to increase or decrease the pump speed based on at least one of the plurality of mass flow values and at least one of the plurality of pressure values.
 9. The system of claim 8 wherein the ECU is further configured to: determine a temperature control signal corresponding to a desired temperature of the fluid at a fuel cell inlet or a fuel cell outlet of the fuel cell stack; calculate a desired pump speed of the pump based on the temperature control signal, at least one of the plurality of mass flow values, and at least one of the plurality of pressure values; and control the pump to increase or decrease the pump speed to be equal to the desired pump speed.
 10. The system of claim 8 further comprising a flow splitter configured to split the fluid into a first fluid flow and a second fluid flow, wherein: the pipe includes a first pipe configured to receive the first fluid flow and a second pipe configured to receive the second fluid flow; and the ECU is further configured to calculate a first pipe mass flow of the first fluid flow through the first pipe and a second pipe mass flow of the second fluid flow through the second pipe based on previously-determined flow resistances of the first pipe and of the second pipe.
 11. The system of claim 8 further comprising a reservoir configured to store the fluid at a reservoir pressure, wherein the memory is further configured to store a lookup table usable to identify a current reservoir pressure of the fluid in the reservoir, and the ECU is further configured to: identify the current reservoir pressure of the fluid in the reservoir; and calculate the plurality of pressure values further based on the current reservoir pressure.
 12. The system of claim 8 wherein the ECU is further configured to: calculate a plurality of density values each corresponding to a density of the fluid through the fuel cell stack, the pump, or the pipe; calculate a plurality of specific heat values each corresponding to a specific heat of the fluid through the fuel cell stack, the pump, or the pipe; and control the pump to increase or decrease the pump speed based on at least one of the plurality of density values and at least one of the plurality of specific heat values.
 13. The system of claim 8 wherein the ECU is further configured to calculate a plurality of temperature values each corresponding to a temperature of the fluid at the outlet of the pump or the pipe based on a previously-determined temperature value at the outlet and the model of the fuel cell circuit.
 14. The system of claim 8 wherein the ECU is further configured to calculate an amount of heat generated by the fuel cell stack and to control the pump to increase or decrease the pump speed further based on the amount of heat generated by the fuel cell stack.
 15. A method for heating or cooling a fuel cell circuit of a vehicle comprising: storing, in a memory, a model of the fuel cell circuit; determining, by the ECU, a temperature control signal corresponding to a desired temperature of a fluid within the fuel cell circuit at a fuel cell inlet or a fuel cell outlet of a fuel cell stack of the fuel cell circuit; calculating, by an electronic control unit (ECU), a plurality of temperature values each corresponding to a fluid temperature of fluid at an outlet of a component of the fuel cell circuit based on a previously-determined temperature value at the outlet, a previously-determined heat transfer value corresponding to heat transfer of the component, and the model of the fuel cell circuit; and controlling, by the ECU, an actuator position of an actuator to increase or decrease the desired temperature based on the plurality of temperature values and the temperature control signal.
 16. The method of claim 15 wherein the component includes at least one of a pipe, the fuel cell stack, a radiator, an intercooler, or a pump.
 17. The method of claim 15 further comprising setting, by the ECU, an inlet temperature of the component to be equal to the fluid temperature at the outlet of an adjacent upstream component, wherein calculating the plurality of temperature values further includes calculating the plurality of temperature values further based on the inlet temperature of the component.
 18. The method of claim 17 further comprising detecting, by a temperature sensor, a fuel cell outlet temperature of the fluid at the fuel cell outlet, wherein calculating the plurality of temperature values further includes calculating the fluid temperature at an adjacent downstream component based on the fuel cell outlet temperature.
 19. The method of claim 15 further comprising calculating, by the ECU, a plurality of pressure values each corresponding to an outlet pressure of the fluid at the outlet of the component, wherein calculating the plurality of temperature values further includes calculating the plurality of temperature values further based on the plurality of pressure values.
 20. The method of claim 19 further comprising calculating, by the ECU, a plurality of mass flow values each corresponding to a mass flow of the fluid through the component, wherein calculating the plurality of pressure values includes calculating the plurality of pressure values based on the plurality of mass flow values. 